2024-07-16T21:32:00+02:00
https://www.carmin.tv/fr/oai
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-4-4
2024-07-05T18:16:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-4-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-their-gauging-in-2d-cfts-4-4
Generalized symmetries and their gauging in 2d CFTs (4/4)
video/mp4
IHES
After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.
2024-07-05T00:00:00+02:00
Yifan Wang
conformal field theory, non-invertible symmetries, fusion category, generalized gauging, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-6e12d1e86dedd8ba024d5244f6142e0e.jpg
oai:carmin.tv:non-invertible-symmetries-in-one-dimensional-quantum-lattice-models
2024-07-05T18:16:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:non-invertible-symmetries-in-one-dimensional-quantum-lattice-models
https://www.carmin.tv/fr/video/non-invertible-symmetries-in-one-dimensional-quantum-lattice-models
Non-invertible symmetries in one-dimensional quantum lattice models
video/mp4
IHES
We will study a lattice realisation of the Symmetry Topological Field Theory (SymTFT) picture for one-dimensional quantum models. We will exploit this picture to study lattice models with non-invertible symmetries, discuss generalised gauging, and construct renormalisation group fixed points of gapped symmetric phases.
2024-07-05T00:00:00+02:00
Clément Delcamp
Generalised symmetry, Lattice models, fusion category, Module category, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-dbd63c9840e8198442c22b942620efc8.jpg
oai:carmin.tv:string-theory-symmetries-and-anomalies-4-4
2024-07-05T20:26:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:string-theory-symmetries-and-anomalies-4-4
https://www.carmin.tv/fr/video/string-theory-symmetries-and-anomalies-4-4
String theory, symmetries and anomalies (4/4)
video/mp4
IHES
I will review some aspects of anomalies of d-dimensional QFTs
from a modern viewpoint (in terms of a d+1 dimensional anomaly theory,
the "anomaly theory"), how symmetries can be described in a related way
in terms of a d+1 dimensional topological field theory (the "SymTFT")
and how these d+1 theories arise from string theory.
2024-07-05T00:00:00+02:00
Inaki Garcia Etxebarria
String theory, symmetries, anomalies, branes, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-d490fb3f3ef6c1fbffb737810cfee966.jpg
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-3-4
2024-07-04T18:06:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-3-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-their-gauging-in-2d-cfts-3-4
Generalized symmetries and their gauging in 2d CFTs (3/4)
video/mp4
IHES
After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.
2024-07-04T00:00:00+02:00
Yifan Wang
conformal field theory, non-invertible symmetries, fusion category, generalized gauging, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-a8d7caad6a4f83b44fe19f7cc59da1ed.jpg
oai:carmin.tv:string-theory-symmetries-and-anomalies-3-4
2024-07-04T18:08:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:string-theory-symmetries-and-anomalies-3-4
https://www.carmin.tv/fr/video/string-theory-symmetries-and-anomalies-3-4
String theory, symmetries and anomalies (3/4)
video/mp4
IHES
I will review some aspects of anomalies of d-dimensional QFTs
from a modern viewpoint (in terms of a d+1 dimensional anomaly theory,
the "anomaly theory"), how symmetries can be described in a related way
in terms of a d+1 dimensional topological field theory (the "SymTFT")
and how these d+1 theories arise from string theory.
2024-07-04T00:00:00+02:00
Inaki Garcia Etxebarria
String theory, symmetries, anomalies, branes, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-cbaf2684f8f6ee4fdc26b4c630dd2bdd.jpg
oai:carmin.tv:nonrelativistic-conformal-field-theory-2-2
2024-07-04T20:16:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:nonrelativistic-conformal-field-theory-2-2
https://www.carmin.tv/fr/video/nonrelativistic-conformal-field-theory-2-2
Nonrelativistic conformal field theory (2/2)
video/mp4
IHES
We will review the notions of Schrödinger symmetry and nonrelativistic conformal field theory, in particular the restrictions that Schrödinger symmetry imposes on correlation function and the operator-state correspondence. We will then consider the most important example of NRCFT --- fermions at unitarity, and derive physical consequences of the formalism.
2024-07-04T00:00:00+02:00
Dam Thanh Son
conformal field theory, unitarity fermions, Schroedinger symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-7737a6599a8771c1e7c90f19e9c1c013.jpg
oai:carmin.tv:string-theory-symmetries-and-anomalies-2-4
2024-07-03T18:06:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:string-theory-symmetries-and-anomalies-2-4
https://www.carmin.tv/fr/video/string-theory-symmetries-and-anomalies-2-4
String theory, symmetries and anomalies (2/4)
video/mp4
IHES
I will review some aspects of anomalies of d-dimensional QFTs
from a modern viewpoint (in terms of a d+1 dimensional anomaly theory,
the "anomaly theory"), how symmetries can be described in a related way
in terms of a d+1 dimensional topological field theory (the "SymTFT")
and how these d+1 theories arise from string theory.
2024-07-03T00:00:00+02:00
Inaki Garcia Etxebarria
String theory, symmetries, anomalies, branes, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-60b28d14b1b11391a0c394ef5d6632e4.jpg
oai:carmin.tv:non-invertible-symmetries-3-3
2024-07-03T18:08:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:non-invertible-symmetries-3-3
https://www.carmin.tv/fr/video/non-invertible-symmetries-3-3
Non-invertible Symmetries (3/3)
video/mp4
IHES
I will review aspects of non-invertible symmetries and their relations to anomalies in lattice and continuum field theories. Examples include the Kramers-Wannier symmetry in the quantum Ising lattice model, and the non-invertible chiral symmetry in the 3+1 QED.
2024-07-03T00:00:00+02:00
Shu-Heng Shao
quantum field theory, symmetry, topological field theory, anomaly, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-25da2a864018f7ded583302abc176040.jpg
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-2-4
2024-07-02T18:36:03+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-2-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-their-gauging-in-2d-cfts-2-4
Generalized symmetries and their gauging in 2d CFTs (2/4)
video/mp4
IHES
After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.
2024-07-02T00:00:00+02:00
Yifan Wang
conformal field theory, non-invertible symmetries, fusion category, generalized gauging, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-e2363065ac1d82ec7336627c10d27e1b.jpg
oai:carmin.tv:non-invertible-symmetries-2-3
2024-07-02T18:56:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:non-invertible-symmetries-2-3
https://www.carmin.tv/fr/video/non-invertible-symmetries-2-3
Non-invertible Symmetries (2/3)
video/mp4
IHES
I will review aspects of non-invertible symmetries and their relations to anomalies in lattice and continuum field theories. Examples include the Kramers-Wannier symmetry in the quantum Ising lattice model, and the non-invertible chiral symmetry in the 3+1 QED.
2024-07-02T00:00:00+02:00
Shu-Heng Shao
quantum field theory, symmetry, topological field theory, anomaly, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-b00424422d42c3a4c36332f0468b8fe7.jpg
oai:carmin.tv:string-theory-symmetries-and-anomalies-1-4
2024-07-02T19:46:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:string-theory-symmetries-and-anomalies-1-4
https://www.carmin.tv/fr/video/string-theory-symmetries-and-anomalies-1-4
String theory, symmetries and anomalies (1/4)
video/mp4
IHES
I will review some aspects of anomalies of d-dimensional QFTs
from a modern viewpoint (in terms of a d+1 dimensional anomaly theory,
the "anomaly theory"), how symmetries can be described in a related way
in terms of a d+1 dimensional topological field theory (the "SymTFT")
and how these d+1 theories arise from string theory.
2024-07-02T00:00:00+02:00
Inaki Garcia Etxebarria
String theory, symmetries, anomalies, branes, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-20b7e9007631ccf2a7ccad2306e2ccb1.jpg
oai:carmin.tv:non-invertible-symmetries-1-3
2024-07-01T16:46:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:non-invertible-symmetries-1-3
https://www.carmin.tv/fr/video/non-invertible-symmetries-1-3
Non-invertible Symmetries (1/3)
video/mp4
IHES
I will review aspects of non-invertible symmetries and their relations to anomalies in lattice and continuum field theories. Examples include the Kramers-Wannier symmetry in the quantum Ising lattice model, and the non-invertible chiral symmetry in the 3+1 QED.
2024-07-01T00:00:00+02:00
Shu-Heng Shao
quantum field theory, symmetry, topological field theory, anomaly, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-02390f72922464e0fbddcef5f4ff8589.jpg
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-1-4
2024-07-01T16:48:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-their-gauging-in-2d-cfts-1-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-their-gauging-in-2d-cfts-1-4
Generalized symmetries and their gauging in 2d CFTs (1/4)
video/mp4
IHES
After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.
2024-07-01T00:00:00+02:00
Yifan Wang
conformal field theory, non-invertible symmetries, fusion category, generalized gauging, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-177d27c13be199b45a89c35691389723.jpg
oai:carmin.tv:nonrelativistic-conformal-field-theory-1-2
2024-07-01T20:06:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:nonrelativistic-conformal-field-theory-1-2
https://www.carmin.tv/fr/video/nonrelativistic-conformal-field-theory-1-2
Nonrelativistic conformal field theory (1/2)
video/mp4
IHES
We will review the notions of Schrödinger symmetry and nonrelativistic conformal field theory, in particular the restrictions that Schrödinger symmetry imposes on correlation function and the operator-state correspondence. We will then consider the most important example of NRCFT --- fermions at unitarity, and derive physical consequences of the formalism.
2024-07-01T00:00:00+02:00
Dam Thanh Son
conformal field theory, unitarity fermions, Schroedinger symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-aa277af75f916a9cf98a8381bfd2c75d.jpg
oai:carmin.tv:higher-symmetry-in-particle-physics-3-4
2024-06-28T13:56:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:higher-symmetry-in-particle-physics-3-4
https://www.carmin.tv/fr/video/higher-symmetry-in-particle-physics-3-4
Higher Symmetry in Particle Physics (3/4)
video/mp4
IHES
These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
2024-06-28T00:00:00+02:00
Clay Cordova
particle physics, higher symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-356bbbb27903cda597813cd0d2d78806.jpg
oai:carmin.tv:higher-symmetry-in-particle-physics-4-4
2024-06-28T22:36:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:higher-symmetry-in-particle-physics-4-4
https://www.carmin.tv/fr/video/higher-symmetry-in-particle-physics-4-4
Higher Symmetry in Particle Physics (4/4)
video/mp4
IHES
These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
2024-06-28T00:00:00+02:00
Clay Cordova
particle physics, higher symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-5fe192b5352d8110a30fdffc958167b5.jpg
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-3-4
2024-06-27T10:50:51+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-3-4
https://www.carmin.tv/fr/video/introduction-to-anomalies-in-condensed-matter-physics-3-4
Introduction to anomalies in condensed matter physics (3/4)
video/mp4
IHES
1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
2024-06-26T00:00:00+02:00
Max Metlitski
Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-f0ee38dfb8ebe6f74d06c692ae5b837c.jpg
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-4-4
2024-06-27T10:50:49+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-4-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-phases-of-gauge-theory-4-4
Generalized Symmetries and Phases of Gauge Theory (4/4)
video/mp4
IHES
These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
2024-06-26T00:00:00+02:00
Thomas Dumitrescu
gauge theory, confinement, symmetries, anomalies, SPTs, QCD, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-6e4696108de4bee49c27dc4f3926c7d9.jpg
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-4-4
2024-06-27T17:18:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-4-4
https://www.carmin.tv/fr/video/introduction-to-anomalies-in-condensed-matter-physics-4-4
Introduction to anomalies in condensed matter physics (4/4)
video/mp4
IHES
1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
2024-06-27T00:00:00+02:00
Max Metlitski
Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-ce02f36af871f011cff3c68d0ee5dfc7.jpg
oai:carmin.tv:higher-symmetry-in-particle-physics-1-4
2024-06-27T17:20:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:higher-symmetry-in-particle-physics-1-4
https://www.carmin.tv/fr/video/higher-symmetry-in-particle-physics-1-4
Higher Symmetry in Particle Physics (1/4)
video/mp4
IHES
These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
2024-06-27T00:00:00+02:00
Clay Cordova
particle physics, higher symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-212c7ec16230d2d433444de922615a63.jpg
oai:carmin.tv:higher-symmetry-in-particle-physics-2-4
2024-06-27T23:36:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:higher-symmetry-in-particle-physics-2-4
https://www.carmin.tv/fr/video/higher-symmetry-in-particle-physics-2-4
Higher Symmetry in Particle Physics (2/4)
video/mp4
IHES
These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
2024-06-27T00:00:00+02:00
Clay Cordova
particle physics, higher symmetry, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-1f61741255cf7a84f99a867172875828.jpg
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-2-4
2024-06-25T16:56:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-2-4
https://www.carmin.tv/fr/video/introduction-to-anomalies-in-condensed-matter-physics-2-4
Introduction to anomalies in condensed matter physics (2/4)
video/mp4
IHES
1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
2024-06-25T00:00:00+02:00
Max Metlitski
Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-995bdae26f9c37a443b39f1a8009de0a.jpg
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-2-4
2024-06-25T17:06:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-2-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-phases-of-gauge-theory-2-4
Generalized Symmetries and Phases of Gauge Theory (2/4)
video/mp4
IHES
These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
2024-06-25T00:00:00+02:00
Thomas Dumitrescu
gauge theory, confinement, symmetries, anomalies, SPTs, QCD, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-a7758211ccfa7fde127fa466fd8fd2c8.jpg
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-3-4
2024-06-25T19:46:01+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-3-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-phases-of-gauge-theory-3-4
Generalized Symmetries and Phases of Gauge Theory (3/4)
video/mp4
IHES
These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
2024-06-25T00:00:00+02:00
Thomas Dumitrescu
gauge theory, confinement, symmetries, anomalies, SPTs, QCD, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-3caf3360a60e5f42a0cfc8948f45db97.jpg
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-1-4
2024-06-24T14:46:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:generalized-symmetries-and-phases-of-gauge-theory-1-4
https://www.carmin.tv/fr/video/generalized-symmetries-and-phases-of-gauge-theory-1-4
Generalized Symmetries and Phases of Gauge Theory (1/4)
video/mp4
IHES
These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
2024-06-24T00:00:00+02:00
Thomas Dumitrescu
gauge theory, confinement, symmetries, anomalies, SPTs, QCD, Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-3c4da5aa01d27a702ef3438c84dcc797.jpg
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-1-4
2024-06-24T21:26:02+02:00
videos:institution:ihes
videos:collection:2024-ihes-summer-school-symmetries-and-anomalies-a-modern-take
oai:carmin.tv:introduction-to-anomalies-in-condensed-matter-physics-1-4
https://www.carmin.tv/fr/video/introduction-to-anomalies-in-condensed-matter-physics-1-4
Introduction to anomalies in condensed matter physics (1/4)
video/mp4
IHES
1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
2024-06-24T00:00:00+02:00
Max Metlitski
Researchers, Graduate Students
en
2024 IHES Summer School – Symmetries and Anomalies : a Modern Take / Symmetries play an outsized role in understanding physical phenomena. In quantum systems ranging from condensed matter to high-energy particle physics, symmetries can feature different types of anomalies, which may constrain the dynamics or ruin the model's consistency. This gives important clues on extensions to the Standard Model, or new topological phenomena in quantum materials. Anomalies have played an essential role in the modern developments of supersymmetric quantum field theories as well as string theory. Last but not least, their study has influenced and benefitted from different areas of mathematics and in particular algebraic topology.
This school will introduce students to the physical and mathematical underpinnings of anomalies including its more mathematical aspects on topological quantum field theory and characteristic classes, with a view toward recent applications to topological phases of matter and strongly coupled gauge theories. The overarching idea is to have courses from three points of view that build upon each other: that of a mathematician (TFT, category theory, characteristic classes), a high-energy physicist (chiral anomalies and Hooft anomaly matching), and a condensed matter physicist (symmetry-protected and symmetry-enhanced topological order). The school would be suited to PhD students and postdocs coming from these three fields. We will ensure that with several tracks of exercise sessions revisiting background knowledge in math/hep-th/cond-mat as necessary.
Courses will range from basic aspects of anomalies of continuous flavour symmetries to cutting-edge topics: conformal anomalies, lattice symmetries, CPT symmetries, higher-form symmetries, higher-group symmetries, as well as a categorical point of view thereon. / Zohar Komargodski, Bruno Le Floch, Elli Pomoni, and Masahito Yamazaki / 24/06/2024 - 05/07/2024 / https://indico.math.cnrs.fr/event/11080/
https://www.carmin.tv/uploads/video/video-e96934b6ae5f974150e014165d7cedbe.jpg
oai:carmin.tv:la-science-au-service-de-la-performance-des-sportifs
2024-06-18T16:38:02+02:00
videos:institution:ihes
videos:collection:les-amis-de-lihes
oai:carmin.tv:la-science-au-service-de-la-performance-des-sportifs
https://www.carmin.tv/fr/video/la-science-au-service-de-la-performance-des-sportifs
La science au service de la performance des sportifs
video/mp4
IHES
Pourquoi les sprinteurs décélèrent-ils avant de passer la ligne d’arrivée ?
Pourquoi vaut-il mieux courir derrière quelqu’un ?
Comment ajuster au mieux sa vitesse pour faire le meilleur temps ?
Cela dépend de l’effort fourni, de l’énergie dépensée, de la motivation car l’être
humain n’est pas un robot et son mouvement est commandé par son cerveau.
À ces questions et quelques autres (Pourquoi la balle de golf a-t-elle des alvéoles ?
Pourquoi nage-t-on mieux légèrement sous l’eau), Amandine Aftalion répond en
s’appuyant sur des notions de physique et de mathématiques, présentées de
façon simple et agréable, et nous permet de mieux comprendre quelques règles
pour améliorer la pratique sportive.
2024-06-13T00:00:00+02:00
Amandine Aftalion
General Public
fr
https://www.carmin.tv/uploads/video/video-94cc6cd9a034cebc50fa114d627a07e3.jpg
oai:carmin.tv:dimension-independent-functional-inequalities-on-sub-riemannian-manifolds
2024-06-18T16:38:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:dimension-independent-functional-inequalities-on-sub-riemannian-manifolds
https://www.carmin.tv/fr/video/dimension-independent-functional-inequalities-on-sub-riemannian-manifolds
Dimension-independent functional inequalities on sub-Riemannian manifolds
video/mp4
IHES
The talk will review recent results on gradient estimates, reverse Poincare and reverse log Sobolev inequalities on a class of sub-Riemannian manifolds. As for many of such setting curvature bounds are not available, we use different techniques. I will introduce the basics of sub-Riemannian manifolds including their metric structure. Joint work with F. Baudoin, L. Luo and R. Sarkar.
2024-06-05T00:00:00+02:00
Masha Gordina
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-425d23bd6adb8164b3aa8c37ff468f38.jpg
oai:carmin.tv:logarithmic-sobolev-inequalities-on-homogeneous-spaces
2024-06-18T16:38:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:logarithmic-sobolev-inequalities-on-homogeneous-spaces
https://www.carmin.tv/fr/video/logarithmic-sobolev-inequalities-on-homogeneous-spaces
Logarithmic Sobolev inequalities on homogeneous spaces
video/mp4
IHES
We consider sub-Riemannian manifolds which are homogeneous spaces equipped with a sub-Riemannian structure induced by a transitive action by a Lie group. The corresponding sub-Laplacian there is not an elliptic but a hypoelliptic operator. We study logarithmic Sobolev inequalities and show that the logarithmic Sobolev constant can be chosen to depend only on the Lie group acting transitively on such a space but the constant is independent of the action of its isotropy group. This approach allows us to track the dependence of the logarithmic Sobolev constant on the geometry of the underlying space, in particular we show that the constant is independent of the dimension of the underlying spaces in several examples. Based on joint work with M.Gordina.
2024-06-05T00:00:00+02:00
Langbing Luo
Researchers
en
https://www.carmin.tv/uploads/video/video-eb44f668c0c226319e716e2ac8716afc.jpg
oai:carmin.tv:quantum-periods-for-complements
2024-06-17T11:04:02+02:00
videos:institution:ihes
videos:collection:physical-mathematics-celebration-of-albert-schwarzs-70-years-in-science
oai:carmin.tv:quantum-periods-for-complements
https://www.carmin.tv/fr/video/quantum-periods-for-complements
Quantum Periods for Complements
video/mp4
IHES
A polynomial P in two variables defines a one-parameter family of spectral curves which are level sets of P, and the corresponding variation of Hodge structures on 1st cohomology groups of these curves. What happens if one quantizes the algebra of polynomials, i.e. deforms it to the Weyl algebra? I'll explain an approach based on second cohomology of complements to the level sets. In particular, one obtains a cohomological description of WKB series for Bohr-Sommefeld quantization rules. This is joint work with A.Soibelman.
2024-06-14T00:00:00+02:00
Maxim Kontsevich
Researchers
en
Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science / Albert Schwarz started as a topologist/geometer in the early '50s, then in the '70s he began an exploration of mathematical aspects of quantum field theory and made numerous seminal contributions to this subject. He has been a regular visitor to IHES since 1995 and was involved in many significant collaborations. This May he will give a short course on his recent research. The mini-conference is a tribute to the 70th anniversary of Schwarz's remarkable scientific career by several of his friends and colleagues. / Anton Kapustin, Maxim Kontsevich / 14/06/2024 - 14/06/2024 / https://indico.math.cnrs.fr/event/11928/
https://www.carmin.tv/uploads/video/video-18b6513ef979a3a7105604d6f92676cc.jpg
oai:carmin.tv:inclusive-scattering-matrix
2024-06-15T20:28:03+02:00
videos:institution:ihes
videos:collection:physical-mathematics-celebration-of-albert-schwarzs-70-years-in-science
oai:carmin.tv:inclusive-scattering-matrix
https://www.carmin.tv/fr/video/inclusive-scattering-matrix
Inclusive Scattering Matrix
video/mp4
IHES
Inclusive scattering matrix closely related to inclusive cross-sections is defined in much more general situations than conventional scattering matrix. It contains the same information when the latter is well defined. It seems that the most natural description of scattering in quantum electrodynamics is based on inclusive scattering matrix.
I'll discuss the general definition of inclusive scattering matrix in the framework of geometric approach to quantum theory and its expression in terms of generalized Green functions that appear in Keldysh formalism. I'll briefly explain the formalism of $L$-functionals and the definition of inclusive scattering matrix in terms of adiabatic $S$-matrix in this formalism.
2024-06-14T00:00:00+02:00
Albert Schwarz
Researchers
en
Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science / Albert Schwarz started as a topologist/geometer in the early '50s, then in the '70s he began an exploration of mathematical aspects of quantum field theory and made numerous seminal contributions to this subject. He has been a regular visitor to IHES since 1995 and was involved in many significant collaborations. This May he will give a short course on his recent research. The mini-conference is a tribute to the 70th anniversary of Schwarz's remarkable scientific career by several of his friends and colleagues. / Anton Kapustin, Maxim Kontsevich / 14/06/2024 - 14/06/2024 / https://indico.math.cnrs.fr/event/11928/
https://www.carmin.tv/uploads/video/video-eb9320b5269dc4eb768ce3fda2968ace.jpg
https://www.carmin.tv/uploads/document/Slides-Schwarz70.pdf
oai:carmin.tv:modularity-of-donaldson-thomas-invariants-on-calabi-yau-threefolds
2024-06-15T20:28:04+02:00
videos:institution:ihes
videos:collection:physical-mathematics-celebration-of-albert-schwarzs-70-years-in-science
oai:carmin.tv:modularity-of-donaldson-thomas-invariants-on-calabi-yau-threefolds
https://www.carmin.tv/fr/video/modularity-of-donaldson-thomas-invariants-on-calabi-yau-threefolds
Modularity of Donaldson-Thomas Invariants on Calabi-Yau Threefolds
video/mp4
IHES
Donaldson-Thomas invariants are the mathematical incarnation of BPS indices counting black hole micro-states in string compactifications. They are notoriously difficult to compute, and subject to wall-crossing phenomena. String dualities predict that generating series of DT invariants counting D4-D2-D0 black holes should have modular (or more generally mock modular) behavior. For one-parameter CY threefolds such as the quintic, one may compute the first few terms in the generating series using vanishing theorems and wall-crossing formulae,and find a unique modular completion. This in turn allows to predict new Gopakumar-Vafa invariants, and determine the topological string amplitude to higher genus than hitherto possible. Based on work in collaboration with Sergey Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm and Thorsten Schimmanek.
2024-06-14T00:00:00+02:00
Boris Pioline
Researchers
en
Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science / Albert Schwarz started as a topologist/geometer in the early '50s, then in the '70s he began an exploration of mathematical aspects of quantum field theory and made numerous seminal contributions to this subject. He has been a regular visitor to IHES since 1995 and was involved in many significant collaborations. This May he will give a short course on his recent research. The mini-conference is a tribute to the 70th anniversary of Schwarz's remarkable scientific career by several of his friends and colleagues. / Anton Kapustin, Maxim Kontsevich / 14/06/2024 - 14/06/2024 / https://indico.math.cnrs.fr/event/11928/
https://www.carmin.tv/uploads/video/video-c30fbe94e7b70e91b42ab74db726b64f.jpg
oai:carmin.tv:prime-knots-and-the-adele-class-space
2024-06-15T21:34:03+02:00
videos:institution:ihes
videos:collection:physical-mathematics-celebration-of-albert-schwarzs-70-years-in-science
oai:carmin.tv:prime-knots-and-the-adele-class-space
https://www.carmin.tv/fr/video/prime-knots-and-the-adele-class-space
Prime, Knots and the Adele Class Space
video/mp4
IHES
We show that the scaling site and its periodic orbits of length log p offer a geometric framework for the well-known analogy between primes and knots. The role of the maximal abelian cover of the scaling site is played by the adele class space which is the quotient of adeles by the action of rational numbers by multiplication. The inverse image of the periodic orbit $C_p$ is canonically isomorphic to the mapping torus of the multiplication by the Frobenius at $p$ in the abelianized étale fundamental group of the spectrum of the ring $Z$ localized at $p$, thus exhibiting the linking of p with all other primes. We give a functorial construction of finite covers of the scaling site associated to finite abelian extension of $Q$. These covers share the same ramification as the field extension, and the monodromy of the periodic orbit $C_p$ in the cover corresponds to the Frobenius$(p)$ element of the Galois group. This is joint work with C. Consani.
2024-06-14T00:00:00+02:00
Alain Connes
Researchers
en
Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science / Albert Schwarz started as a topologist/geometer in the early '50s, then in the '70s he began an exploration of mathematical aspects of quantum field theory and made numerous seminal contributions to this subject. He has been a regular visitor to IHES since 1995 and was involved in many significant collaborations. This May he will give a short course on his recent research. The mini-conference is a tribute to the 70th anniversary of Schwarz's remarkable scientific career by several of his friends and colleagues. / Anton Kapustin, Maxim Kontsevich / 14/06/2024 - 14/06/2024 / https://indico.math.cnrs.fr/event/11928/
https://www.carmin.tv/uploads/video/video-385c19af924e1af0b5c108b305a4a3e8.jpg
oai:carmin.tv:topological-invariants-of-gapped-states-and-t-hooft-anomalies
2024-06-15T21:36:02+02:00
videos:institution:ihes
videos:collection:physical-mathematics-celebration-of-albert-schwarzs-70-years-in-science
oai:carmin.tv:topological-invariants-of-gapped-states-and-t-hooft-anomalies
https://www.carmin.tv/fr/video/topological-invariants-of-gapped-states-and-t-hooft-anomalies
Topological Invariants of Gapped States and ’t Hooft Anomalies
video/mp4
IHES
Recently, an approach to constructing topological invariants of gapped ground-states of lattice systems has been developed in our joint work with N. Sopenko. It applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying interactions and employs C*-algebraic techniques. In this talk I will explain an interpretation of these invariants as obstructions to gauging, i.e. to promoting a symmetry to a local symmetry. The key observation is that locality on a lattice is an asymptotic notion sensitive only to the large-scale geometry of the support set. Following Kashiwara and Schapira, one can encode locality using a natural Grothendieck topology on a category of semilinear subsets of Eucludean space. Infinitesimal symmetries of a gapped state form a cosheaf over the corresponding site, and the topological invariants are encoded in its Cech complex.
2024-06-14T00:00:00+02:00
Anton Kapustin Kapustin
Researchers
en
Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science / Albert Schwarz started as a topologist/geometer in the early '50s, then in the '70s he began an exploration of mathematical aspects of quantum field theory and made numerous seminal contributions to this subject. He has been a regular visitor to IHES since 1995 and was involved in many significant collaborations. This May he will give a short course on his recent research. The mini-conference is a tribute to the 70th anniversary of Schwarz's remarkable scientific career by several of his friends and colleagues. / Anton Kapustin, Maxim Kontsevich / 14/06/2024 - 14/06/2024 / https://indico.math.cnrs.fr/event/11928/
https://www.carmin.tv/uploads/video/video-ce978edd613aaf296a26d9cf421136dc.jpg
oai:carmin.tv:50th-anniversary-of-the-ihes-launch-of-celebrations
2024-06-13T11:38:41+02:00
videos:institution:ihes
videos:collection:2008-50th-anniversary-of-the-ihes
oai:carmin.tv:50th-anniversary-of-the-ihes-launch-of-celebrations
https://www.carmin.tv/fr/video/50th-anniversary-of-the-ihes-launch-of-celebrations
50th anniversary of the IHES: launch of celebrations
video/mp4
IHES
The official launch of the celebrations of the IHÉS 50th anniversary took place on 27 March in the afternoon in the Marilyn & James Simons Conference Centre, in the presence of Valérie PÉCRESSE, French Minister for Higher Education and Research, many elected representatives and heads of neighbouring scientific institutions, together with Didier and Jean-Loup MOTCHANE, the two sons of the Institute’s founder.
Cécile DEWITT-MORETTE (Emerita Professor at the University of Texas) opened the ceremony by recalling historic moments in the Institute’s creation and in particular the famous episode of the meeting between Léon MOTCHANE and Robert OPPENHEIMER.
Presentations followed by David RUELLE (honorary professor at IHÉS), Yuri MANIN (Max-Planck Institut für Mathematik and Northwestern University), David MUMFORD (Brown University) Joseph TAYLOR (Princeton University) and Philippe LAGAYETTE (Chairman of the Board of Directors of IHÉS).
Valérie PÉCRESSE, who honoured the Institute with her presence, made the closing speech. She then inaugurated the travelling exhibition The Unravelers, based on the book by Jean-François DARS, Annick LESNE and Anne PAPILLAULT, published by Éditions Belin and which had just become available in bookshops. She was also able to congratulate Jacques TITS, who was keen to share this event with IHÉS. The official announcement of the 2008 Abel Prize jointly to John GRIGGS-THOMPSON and himself, had been announced that very morning.
2008-03-27T00:00:00+01:00
Yuri Manin
David Ruelle
Cécile Dewitt-Morette
David Mumford
Joseph Taylor
Philippe Lagayette
Valérie Pécresse
General Public
en
2008 - 50th anniversary of the IHES / The year 2008 marked the 50th anniversary of the IHÉS. To celebrate this event several conferences were organized throughout the world, in France, in Japan, in the United States. In particular, IHÉS hosted a conference on mathematics in May and on theoretical physics in June. / 27/03/2008 - 20/06/2028
https://www.carmin.tv/uploads/video/video-9fc07e33a353117e1cc473bef44b218c.jpg
oai:carmin.tv:topological-recursion-a-recursive-way-of-counting-surfaces
2024-06-09T14:26:34+02:00
videos:institution:ihes
videos:collection:matrix-models-for-quantum-systems-special-day-of-the-seed-seminar-of-mathematics-and-physics
oai:carmin.tv:topological-recursion-a-recursive-way-of-counting-surfaces
https://www.carmin.tv/fr/video/topological-recursion-a-recursive-way-of-counting-surfaces
Topological Recursion: a recursive way of counting surfaces
video/mp4
IHES
Enumerating various kinds of surfaces is an important goal in combinatorics of maps, enumerative geometry, string theory, statistical physics, and other areas of mathematics or theoretical physics. For example the famous Mirzakhani's recursion is about enumerating hyperbolic surfaces. It is often easier to enumerate planar surfaces, with the lowest topologies (disc, cylinder), and the question is how to enumerate surfaces of higher genus and with more boundaries. Many of the surface enumeration problems, satisfy a universal recursion, known as the "topological recursion", which, from the enumeration of discs and cylinders, gives all the other topologies. Moreover this recursion has many beautiful mathematical properties by itself, and allows to make the link with other areas of mathematics and physics, in particular integrable systems, random matrices, and many others.
2024-06-07T00:00:00+02:00
Bertrand Eynard
intégrales de matrices, surfaces de Riemann, équations de récurrence pour des cartes, Researchers
en
Matrix Models for Quantum Systems – Special Day of the Seed Seminar of Mathematics and Physics / The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, with both online and in-person events. It is holding a special day on Matrix models for quantum systems at IHES, with contributions from Guillaume Aubrun, Philippe Biane, Bertrand Eynard and Vladimir Kazakov. / Ariane Carrance, Matteo D’Achille, Edoardo Lauria / 07/06/2024 - 07/06/2024 / https://indico.math.cnrs.fr/event/12052/
https://www.carmin.tv/uploads/video/video-2e012fd79664512e8d3e43f8c74c23e6.jpg
oai:carmin.tv:entangleability-of-cones
2024-06-10T00:50:37+02:00
videos:institution:ihes
videos:collection:matrix-models-for-quantum-systems-special-day-of-the-seed-seminar-of-mathematics-and-physics
oai:carmin.tv:entangleability-of-cones
https://www.carmin.tv/fr/video/entangleability-of-cones
Entangleability of Cones
video/mp4
IHES
We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones $C1, C2$, their minimal tensor product is the cone generated by products of the form $x1 \otimes x2$, where $x1 \in C1$ and $x2 \in C2$, while their maximal tensor product is the set of tensors that are positive under all product functionals $f1 \otimes f2$, where $f1$ is positive on $C1$ and $f2$ is positive on $C2$. Our proof techniques involve a mix of convex geometry, elementary algebraic topology, and computations inspired by quantum information theory. Our motivation comes from the foundations of physics: as an application, we show that any two non-classical systems modelled by general probabilistic theories can be entangled.
2024-06-07T00:00:00+02:00
Guillaume Aubrun
produits tensoriels de cônes, intricabilité, théories probabilistes générales, Researchers
en
Matrix Models for Quantum Systems – Special Day of the Seed Seminar of Mathematics and Physics / The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, with both online and in-person events. It is holding a special day on Matrix models for quantum systems at IHES, with contributions from Guillaume Aubrun, Philippe Biane, Bertrand Eynard and Vladimir Kazakov. / Ariane Carrance, Matteo D’Achille, Edoardo Lauria / 07/06/2024 - 07/06/2024 / https://indico.math.cnrs.fr/event/12052/
https://www.carmin.tv/uploads/video/video-96a120952f6be5e2c650ca849fa87af7.jpg
oai:carmin.tv:quantum-exclusion-process-random-matrices-and-free-cumulants
2024-06-10T01:56:38+02:00
videos:institution:ihes
videos:collection:matrix-models-for-quantum-systems-special-day-of-the-seed-seminar-of-mathematics-and-physics
oai:carmin.tv:quantum-exclusion-process-random-matrices-and-free-cumulants
https://www.carmin.tv/fr/video/quantum-exclusion-process-random-matrices-and-free-cumulants
Quantum Exclusion Process, Random Matrices and Free Cumulants
video/mp4
IHES
The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. I will explain how free cumulants, which are quantities arising in free probability and random matrix theory, encode the fluctuations of the invariant measure of this process when the number of sites goes to infinity.
2024-06-07T00:00:00+02:00
Philippe Biane
processus d'exclusion, cumulants libres, associaèdres, Researchers
en
Matrix Models for Quantum Systems – Special Day of the Seed Seminar of Mathematics and Physics / The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, with both online and in-person events. It is holding a special day on Matrix models for quantum systems at IHES, with contributions from Guillaume Aubrun, Philippe Biane, Bertrand Eynard and Vladimir Kazakov. / Ariane Carrance, Matteo D’Achille, Edoardo Lauria / 07/06/2024 - 07/06/2024 / https://indico.math.cnrs.fr/event/12052/
https://www.carmin.tv/uploads/video/video-ddc53f277345198787a0aed538ba5fe0.jpg
oai:carmin.tv:matrix-model-for-structure-constants-of-huge-protected-operators-in-n-4-sym-theory-1
2024-06-10T02:56:34+02:00
videos:institution:ihes
videos:collection:matrix-models-for-quantum-systems-special-day-of-the-seed-seminar-of-mathematics-and-physics
oai:carmin.tv:matrix-model-for-structure-constants-of-huge-protected-operators-in-n-4-sym-theory-1
https://www.carmin.tv/fr/video/matrix-model-for-structure-constants-of-huge-protected-operators-in-n-4-sym-theory-1
Matrix Model for Structure Constants of "Huge" Protected Operators in N=4 SYM Theory
video/mp4
IHES
Huge operators in N = 4 SYM theory correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the protected correlation function of three such huge operators when they are given by 1/2 BPS operators , dual to IIB Strings in AdS5 × S 5 . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we transform this matrix model into a 1 + 1 dimensional integrable hydrodynamics problem. A discrete counterpart of this system -– the rational Calogero-Moser Model - helps to numerically solve the problem for general huge operators.
2024-06-07T00:00:00+02:00
Vladimir Kazakov
théorie supersymétrique de Yang-Mills, modèles de matrices, Researchers
en
Matrix Models for Quantum Systems – Special Day of the Seed Seminar of Mathematics and Physics / The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, with both online and in-person events. It is holding a special day on Matrix models for quantum systems at IHES, with contributions from Guillaume Aubrun, Philippe Biane, Bertrand Eynard and Vladimir Kazakov. / Ariane Carrance, Matteo D’Achille, Edoardo Lauria / 07/06/2024 - 07/06/2024 / https://indico.math.cnrs.fr/event/12052/
https://www.carmin.tv/uploads/video/video-c7643b82bedb88dd11d84467ef916d24.jpg
oai:carmin.tv:waists-measured-via-urysohn-width
2024-06-03T11:26:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:waists-measured-via-urysohn-width
https://www.carmin.tv/fr/video/waists-measured-via-urysohn-width
Waists measured via Urysohn width
video/mp4
IHES
The Urysohn width measures the "approximate dimension" of a riemannian manifold by approximating it with a lower-dimensional simplicial complex. Positive scalar curvature conjecturally implies upper bounds on the width. An inductive approach to this conjecture and related ones requires understanding of the following question: If our manifold is sliced into chunks of small approximate dimension, does that imply that the manifold itself has controlled approximate dimension? I will explain a few results in that direction, mostly of negative nature.
2024-05-22T00:00:00+02:00
Alexey Balitsky
Researchers
en
https://www.carmin.tv/uploads/video/video-a18ea1bbd4765db76f9febbe1c3588d9.jpg
oai:carmin.tv:width-scalar-curvature-and-macroscopic-scalar-curvature
2024-06-03T11:26:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:width-scalar-curvature-and-macroscopic-scalar-curvature
https://www.carmin.tv/fr/video/width-scalar-curvature-and-macroscopic-scalar-curvature
Width, scalar curvature and macroscopic scalar curvature
video/mp4
IHES
Gromov observed a surprising interplay between positive scalar curvature and a simple condition on the volumes of balls of fixed radius known as positive macroscopic scalar curvature. I will talk about some results about Urysohn width and lengths of closed geodesics in PSC and PMSC spaces, and how ideas travel back and forth between these two worlds.
2024-05-22T00:00:00+02:00
Yevgeny Liokumovich
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-c63f4d3d2f990b1f7d8a21aa8e35f354.jpg
oai:carmin.tv:on-spectra-of-laplace-and-dirac-operators-on-noncompact-manifolds
2024-05-28T16:50:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:on-spectra-of-laplace-and-dirac-operators-on-noncompact-manifolds
https://www.carmin.tv/fr/video/on-spectra-of-laplace-and-dirac-operators-on-noncompact-manifolds
On spectra of Laplace and Dirac operators on noncompact manifolds
video/mp4
IHES
In this talk we give an overview over results on the spectrum of Laplace and Dirac operators on complete manifolds. After a general introduction to the different types of spectra, we review several results on spectra for special behaviors of the manifolds at infinity. At the end, we also discuss the influence of some additional potentials.
2024-05-08T00:00:00+02:00
Nadine Große
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-4433ec0d5cfe2ddae06c46c84d7f6517.jpg
oai:carmin.tv:on-the-l-p-spectrum
2024-05-28T16:50:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:on-the-l-p-spectrum
https://www.carmin.tv/fr/video/on-the-l-p-spectrum
On the $L^p$ spectrum
video/mp4
IHES
In this talk, we will show that the resolvent set of the Laplacian on $L^p$ integrable $k$-forms lies outside a parabola whenever the volume of the manifold has an exponential volume growth rate, removing the requirement on the manifold to be of bounded geometry. Moreover, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the $L^p$-spectrum of the Laplacian on $k$-forms, and we provide a detailed description of the $L^p$ spectrum of the Laplacian on $k$-forms over hyperbolic space. The above results are joint work with Zhiqin Lu. We will also see a recent result with Julie Rowlett for the $L^p$ spectrum of conformally compact manifolds.
2024-05-08T00:00:00+02:00
Nelia Charalambous
Researchers
en
https://www.carmin.tv/uploads/video/video-cecbbe0b4762b8ef470def4eb77eba4b.jpg
oai:carmin.tv:how-can-machine-learning-help-mathematicians-1
2024-05-28T15:23:13+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:how-can-machine-learning-help-mathematicians-1
https://www.carmin.tv/fr/video/how-can-machine-learning-help-mathematicians-1
How can Machine Learning Help Mathematicians
video/mp4
IHES
Large Language models have known large successes in recent years. This naturally raises the question: can AI assist mathematicians in solving open problems in mathematics? We will explore how a language model can be trained to learn a mathematical intuition on open problems and guess candidate solutions, with a focus on a few examples. We will also explore the application of LLM to automated theorem proving with an online training procedure and discuss new perspectives in the area.
2024-05-23T00:00:00+02:00
Amaury Hayat
control theory, transformers, AI for mathematics, Lyapunov functions, automated theorem proving, LLM, tree search, Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-77a25342cd081d8b2646d0feb97abad5.jpg
oai:carmin.tv:how-can-machine-learning-help-mathematicians
2024-05-25T22:08:01+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:how-can-machine-learning-help-mathematicians
https://www.carmin.tv/fr/video/how-can-machine-learning-help-mathematicians
How can Machine Learning Help Mathematicians
video/mp4
IHES
Large Language models have known large successes in recent years. This naturally raises the question: can AI assist mathematicians in solving open problems in mathematics? We will explore how a language model can be trained to learn a mathematical intuition on open problems and guess candidate solutions, with a focus on a few examples. We will also explore the application of LLM to automated theorem proving with an online training procedure and discuss new perspectives in the area.
2024-05-23T00:00:00+02:00
Amaury Hayat
Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-0b6c6f5416045e71f375cf7f2b638a8a.jpg
oai:carmin.tv:synthetic-data-friend-or-foe-in-the-age-of-scaling
2024-05-25T22:08:01+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:synthetic-data-friend-or-foe-in-the-age-of-scaling
https://www.carmin.tv/fr/video/synthetic-data-friend-or-foe-in-the-age-of-scaling
Synthetic Data – Friend or Foe in the Age of Scaling?
video/mp4
IHES
As AI and LLM model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data.
In this talk we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the LLM Llama2.
2024-05-23T00:00:00+02:00
Julia Kempe
synthetic data, model collapse, iterative retraining, scaling laws, kernel ridge regression., Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-e10233ca6ab80f7e06b721be0a864323.jpg
oai:carmin.tv:a-first-approximation-to-the-mathematical-structure-computed-by-large-language-models
2024-05-25T22:10:02+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:a-first-approximation-to-the-mathematical-structure-computed-by-large-language-models
https://www.carmin.tv/fr/video/a-first-approximation-to-the-mathematical-structure-computed-by-large-language-models
A First Approximation to the Mathematical Structure Computed by Large Language Models
video/mp4
IHES
Large Language Models are transformer neural networks which are trained to produce a probability distribution on the possible next words to given texts in a corpus, in such a way that the most likely word predicted, is the actual word in the training text.
We will explain what is the mathematical structure defined by such conditional probability distributions of text extensions. Changing the viewpoint from probabilities to -log probabilities we observe that the data of text extensions are encoded in a directed (non-symmetric) metric structure defined on the space of texts ${\mathcal L}$. We then construct a directed metric polyhedron $P({\mathcal L})$, in which ${\mathcal L}$ is isometrically embedded as generators of certain special extremal rays. Each such generator encodes extensions of a text along with the corresponding probabilities.
Moreover $P({\mathcal L})$ is $(\min, +)$ (i.e. tropically) generated by the text extremal rays and is the image of a $(\min,+)$ projector (given by the metric on ${\mathcal L}$). This leads to a duality theorem relating the polyhedron $P({\mathcal L})$ defined by text extensions to one defined by text restrictions. We also explain that the generator of the extremal ray corresponding to a text is approximated by a Boltzmann weighted linear combination of generators of extremal rays corresponding to the words making up that text.
The metric space ${\mathcal L}$ can equivalently be considered as an enriched category and then the embedding into $P({\mathcal L})$ is the Yoneda embedding into the category of presheaves. In fact all constructions have categorical meaning (in particular generalizing the familiar view of language as a monoid or as a poset with the subtext order). The categorical interpretations will be explained in parallel.
This is joint work with Stéphane Gaubert.
2024-05-23T00:00:00+02:00
Yiannis Vlassopoulos
tropical geometry, directed metric spaces, enriched categories, Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-db2ea3d74ab038b2533cc195fe3978c4.jpg
oai:carmin.tv:mathematics-as-a-translation-task-the-importance-of-training-distributions
2024-05-25T22:12:01+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:mathematics-as-a-translation-task-the-importance-of-training-distributions
https://www.carmin.tv/fr/video/mathematics-as-a-translation-task-the-importance-of-training-distributions
Mathematics as a Translation Task - the Importance of Training Distributions
video/mp4
IHES
Many problems of mathematics can be set as translation tasks: problems, represented as sentences in some language, are translated into their solutions, by language models trained from synthetic examples. In this setting, we can choose the distribution of problems and solutions we use to train the model. I present examples from three different experiments, which suggest that this can make a large difference in model performance, and provide intuition on the inner workings of transformer models.
2024-05-23T00:00:00+02:00
Francois Charton
Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-5d39c35fd739aa280bb1bd501005d3ed.jpg
oai:carmin.tv:three-problems-in-the-mathematics-of-deep-learning
2024-05-25T22:14:01+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:three-problems-in-the-mathematics-of-deep-learning
https://www.carmin.tv/fr/video/three-problems-in-the-mathematics-of-deep-learning
Three Problems in the Mathematics of Deep Learning
video/mp4
IHES
Neural networks, particularly LLMs, are notoriously poor at algorithmic tasks, such as sorting, shortest path, and even basic arithmetic. Across three papers, we explored the problem of "aligning" architectures to classical computer programs, and showed that this question relates to familiar mathematical concepts: polynomial functors, cohomology, and higher categories.
2024-05-23T00:00:00+02:00
Andrew Dudzik
Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-0f735e33f0a6f52462ecd1ccda43a6f0.jpg
oai:carmin.tv:grounding-llms-in-execution
2024-05-25T22:16:01+02:00
videos:institution:ihes
videos:collection:mathematics-for-and-by-large-language-models
oai:carmin.tv:grounding-llms-in-execution
https://www.carmin.tv/fr/video/grounding-llms-in-execution
Grounding LLMs in Execution
video/mp4
IHES
Large language models (LLMs) are trained in a very simple way. Lots of properties we assign to them are already present in the training data. In this talk we will review how LLMs are trained today, what are new training paradigms that are aiming at grounding those LLMs in the impact of those generations. In the context of code generation, this is for instance groudning the LLM with the feedback of executing its generated code. For Lean proofstep prediction we can use tactics execution feedback similarly. We believe closing the loop between “open” generation and “grouding” with more formal system can bridge the gap between informal and formal LLM usages.
2024-05-23T00:00:00+02:00
Gabriel Synnaeve
Researchers
en
Mathematics for and by Large Language Models / The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how.
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated. / François Charton, Michael Douglas, Yiannis Vlassopoulos / 23/05/2024 - 23/05/2024 / https://indico.math.cnrs.fr/event/11933/
https://www.carmin.tv/uploads/video/video-d51bd7de1a8b5137b5d0fb66c0d19bec.jpg
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-4-4
2024-05-15T11:20:02+02:00
videos:institution:ihes
videos:collection:albert-schwarz-quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-4-4
https://www.carmin.tv/fr/video/quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-4-4
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (4/4)
video/mp4
IHES
The course is based on a minibook that will be published by Springer. The text below is a shortened preface to this book.
In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.
We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green's functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green's functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.
2024-05-14T00:00:00+02:00
Albert Schwarz
QFT, scattering matrix, generalized Green function, geometric approach, L-functionals, Researchers, Graduate Students
en
Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints / 03/05/2024 - 14/05/2024
https://www.carmin.tv/uploads/video/video-bc8c91e9da2ec1fb9047f1c0f9d31821.jpg
https://www.carmin.tv/uploads/document/Lecture4n.pdf
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-3-4
2024-05-10T19:06:02+02:00
videos:institution:ihes
videos:collection:albert-schwarz-quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-3-4
https://www.carmin.tv/fr/video/quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-3-4
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (3/4)
video/mp4
IHES
The course is based on a minibook that will be published by Springer. The text below is a shortened preface to this book.
In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.
We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green's functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green's functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.
2024-05-10T00:00:00+02:00
Albert Schwarz
QFT, scattering matrix, generalized Green function, geometric approach, L-functionals, Researchers, Graduate Students
en
Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints / 03/05/2024 - 14/05/2024
https://www.carmin.tv/uploads/video/video-8c00cbdfcba4a104dc1d6e85d45556a9.jpg
https://www.carmin.tv/uploads/document/Lecture3n.pdf
oai:carmin.tv:geometric-variational-methods-to-not-only-scalar-curvature-problems
2024-05-09T17:46:01+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:geometric-variational-methods-to-not-only-scalar-curvature-problems
https://www.carmin.tv/fr/video/geometric-variational-methods-to-not-only-scalar-curvature-problems
Geometric variational methods to (not only) scalar curvature problems
video/mp4
IHES
In this talk I will review the application of geometric variational problems (e.g. minimal surfaces) to the study of curvature conditions. I will start with the Schoen-Yau dimension descent approach to scalar curvature problems, and discuss recent extensions with applications to other curvature conditions.
2024-04-24T00:00:00+02:00
Chao Li
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-ecee38ca831660ecef2c39d010d97cb7.jpg
oai:carmin.tv:another-aspect-of-gromovs-conjectures
2024-05-09T17:46:01+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:another-aspect-of-gromovs-conjectures
https://www.carmin.tv/fr/video/another-aspect-of-gromovs-conjectures
Another aspect of Gromov’s conjectures
video/mp4
IHES
In this talk, we will discuss some conjectures of Gromov on scalar curvature from the perspective of general relativity, in particular their partial solutions by the positive mass theorem.
2024-04-24T00:00:00+02:00
Tin-Yau Tsang
Researchers
en
https://www.carmin.tv/uploads/video/video-c8742fe61eaa13afcbda44f11579b57d.jpg
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-2-4
2024-05-07T22:16:01+02:00
videos:institution:ihes
videos:collection:albert-schwarz-quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-2-4
https://www.carmin.tv/fr/video/quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-2-4
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (2/4)
video/mp4
IHES
The course is based on a minibook that will be published by Springer. The text below is a shortened preface to this book.
In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.
We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green's functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green's functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.
2024-05-07T00:00:00+02:00
Albert Schwarz
QFT, scattering matrix, generalized Green function, geometric approach, L-functionals, Researchers, Graduate Students
en
Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints / 03/05/2024 - 14/05/2024
https://www.carmin.tv/uploads/video/video-fa41ed5b173ffedbe8c26c92960f6223.jpg
https://www.carmin.tv/uploads/document/Lecture2n.pdf
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-1-4
2024-05-04T19:48:03+02:00
videos:institution:ihes
videos:collection:albert-schwarz-quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints
oai:carmin.tv:quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-1-4
https://www.carmin.tv/fr/video/quantum-mechanics-and-quantum-field-theory-from-algebraic-and-geometric-viewpoints-1-4
Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints (1/4)
video/mp4
IHES
The course is based on a minibook that will be published by Springer. The text below is a shortened preface to this book.
In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.
We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green's functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green's functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.
2024-05-03T00:00:00+02:00
Albert Schwarz
QFT, scattering matrix, generalized Green function, geometric approach, L-functionals, Researchers, Graduate Students
en
Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints / 03/05/2024 - 14/05/2024
https://www.carmin.tv/uploads/video/video-8a147d25f55cb542d9c03208dcc404a9.jpg
https://www.carmin.tv/uploads/document/Lecture1n.pdf
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-4-4
2024-05-03T23:56:01+02:00
videos:institution:ihes
videos:collection:clement-delcamp-topological-symmetry-and-duality-in-quantum-lattice-models
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-4-4
https://www.carmin.tv/fr/video/topological-symmetry-and-duality-in-quantum-lattice-models-4-4
Topological Symmetry and Duality in Quantum Lattice Models (4/4)
video/mp4
IHES
A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.
2024-05-03T00:00:00+02:00
Clément Delcamp
, duality, Generalised symmetry, Topology, Lattice models, Researchers, Graduate Students
en
Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models / 16/04/2024 - 03/05/2024
https://www.carmin.tv/uploads/video/video-9ddabc632cc166f7b6a6dab7245d9b2b.jpg
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-3-4
2024-05-02T18:54:01+02:00
videos:institution:ihes
videos:collection:clement-delcamp-topological-symmetry-and-duality-in-quantum-lattice-models
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-3-4
https://www.carmin.tv/fr/video/topological-symmetry-and-duality-in-quantum-lattice-models-3-4
Topological Symmetry and Duality in Quantum Lattice Models (3/4)
video/mp4
IHES
A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.
2024-04-30T00:00:00+02:00
Clément Delcamp
, duality, Generalised symmetry, Topology, Lattice models, Researchers, Graduate Students
en
Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models / 16/04/2024 - 03/05/2024
https://www.carmin.tv/uploads/video/video-47abe593b2d43059222055dec10396a1.jpg
oai:carmin.tv:vanishing-theorems-in-positive-characteristic
2024-04-28T16:52:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:vanishing-theorems-in-positive-characteristic
https://www.carmin.tv/fr/video/vanishing-theorems-in-positive-characteristic
Vanishing Theorems in Positive Characteristic
video/mp4
IHES
Starting from the seminal book of Hélène Esnault and Eckart Viehweg on vanishing theorems my talk will be centered around vanishing theorems in positive characteristics. The Kodaira and Kawamata—Viehweg vanishing theorems are incredibly useful in Complex geometry but fail in general to be true over fields of positive characteristics. It was long expected that this failure would be pathological and that these theorems still would be true for some important classes of varieties, such as log Fano varieties. It turns out that starting from dimension two there are log Fano varieties which contradict Kodaira vanishing. However, the known constructions have the dimension of the Fano variety increasing with the characteristic of the base field. One could therefore ask if in any given dimension log Fano's satisfy this vanishing theorem in large enough characteristic depending on the dimension? In this direction, joint with Fabio Bernasconi and Justin Lacini we proved that the Kawamata—Viehweg vanishing theorem holds on log del Pezzo surfaces over a perfect field of characteristic p>5.
2024-04-26T00:00:00+02:00
Emelie Arvidsson
Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-5fbf8bca83768efc5e00c89662f6277b.jpg
oai:carmin.tv:weight-filtration-on-log-crystalline-site
2024-04-28T16:52:03+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:weight-filtration-on-log-crystalline-site
https://www.carmin.tv/fr/video/weight-filtration-on-log-crystalline-site
Weight Filtration on Log Crystalline Site
video/mp4
IHES
Let $p$ be a prime. For a family of simple normal crossing log varieties on which p is nilpotent, we construct a filtered complex on certain log crystalline site which gives rise to the weight filtered p-adic Steenbrink complex defined by Mokrane and Nakkajima when we project it to the Zariski site.
2024-04-26T00:00:00+02:00
Atsushi Shiho
weight filtration, simple normal crossing log variety, log crystalline site, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-5f11fc083df2ca8370d76fa56d7365fc.jpg
oai:carmin.tv:integrality-of-the-betti-moduli-space
2024-04-28T16:56:03+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:integrality-of-the-betti-moduli-space
https://www.carmin.tv/fr/video/integrality-of-the-betti-moduli-space
Integrality of the Betti Moduli Space
video/mp4
IHES
This is a report on joint work with Hélène Esnault. Let X be a smooth projective variety over the complex numbers C. Let M be the moduli space of irreducible representations of the topological fundamental group of X of a fixed rank r. Then M is a finite type scheme over the spectrum of the integers Z. We may ask whether M is pure over Z in the sense of Raynaud-Gruson, for example we can ask if the irreducible components of M which dominate Spec(Z) actually surject onto Spec(Z). We will explain what this means, present a weak answer to this question, apply this to exclude some abstract groups as the fundamental groups of smooth projective varieties over C, and we discuss what other phenomena can be studied using the method of proof.
2024-04-26T00:00:00+02:00
Johan de Jong
fundamental groups, local systems, Algebraic varieties, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-83f6faec8ce106901f2da4c691e1416d.jpg
oai:carmin.tv:analytic-prismatization
2024-04-28T16:50:03+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:analytic-prismatization
https://www.carmin.tv/fr/video/analytic-prismatization
Analytic Prismatization
video/mp4
IHES
Prismatic cohomology is a unifying p-adic cohomology of $p$-adic formal schemes. Motivated by questions on locally analytic representations of $p$-adic groups and the $p$-adic Simpson correspondence, an extension of prismatic cohomology to rigid-analytic spaces (over $Q_p$ or over $F_p((t)))$ has been sought. We will explain what form this should take, and our progress on realizing this picture. This includes a degeneration from the analytic Hodge-Tate stack underlying the $p$-adic Simpson correspondence to a similar (analytic) stack related to the Ogus-Vologodsky correspondence in characteristic $p$. This is joint work in progress with Johannes Anschütz, Arthur-César le Bras and Juan Esteban Rodriguez Camargo.
2024-04-25T00:00:00+02:00
Peter Scholze
prismatic cohomology, rigid-analytic varieties, Simpson correspondence, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-ee27ab9c79a79a7d71c3927030054a09.jpg
oai:carmin.tv:local-systems-and-higgs-bundles-in-p-adic-geometry
2024-04-29T13:18:43+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:local-systems-and-higgs-bundles-in-p-adic-geometry
https://www.carmin.tv/fr/video/local-systems-and-higgs-bundles-in-p-adic-geometry
Local systems and Higgs bundles in p-adic geometry
video/mp4
IHES
The classical Corlette--Simpson (CS) correspondence relates local systems on complex varieties to Higgs bundles; it is highly transcendental in nature. Its characteristic p counterpart surprisingly turns out to be purely algebraic: Bezrukavnikov identified de Rham local systems on a smooth variety X over F_p with Higgs bundles twisted by a natural G_m-gerbe on the cotangent bundle T*X. By trivializing the gerbe over suitable loci in T*X using additional choices, Ogus--Vologodsky then recovered an honest CS correspondence (i.e., with untwisted Higgs bundles). In this talk, I'll explain that this story has an exact analog for a smooth rigid space X over a perfectoid p-adic field: (generalized) local systems identify with Higgs bundles twisted by a natural G_m-gerbe on T*X, and honest CS correspondences (as studied by many authors in the last 2 decades) can be recovered by trivializing the gerbe over suitable loci in T*X.
This is joint work in progress with Mingjia Zhang, and is inspired by recent work of Heuer.
2024-04-25T00:00:00+02:00
Bhargav Bhatt
Higgs bundles, local systems, Simpson correspondence, non-abelian p-adic Hodge theory, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-bfcbc33227f151ecbedf921cb747d47b.jpg
oai:carmin.tv:characteristic-classes-of-etale-local-systems
2024-04-26T16:16:04+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:characteristic-classes-of-etale-local-systems
https://www.carmin.tv/fr/video/characteristic-classes-of-etale-local-systems
Characteristic Classes of Étale Local Systems
video/mp4
IHES
Given an étale Z_p-local system of rank n on an algebraic variety X, continuous cohomology classes of the group GL_n(Z_p) give rise to classes in (absolute) étale cohomology of the variety with coefficients in Z_p. These characteristic classes can be thought of as p-adic analogs of Chern-Simons characteristic classes of vector bundles with a flat connection.
For a smooth projective variety over complex numbers, Reznikov proved that the usual Chern-Simons classes in degrees >1 of all C-local systems are torsion. It turns out that characteristic classes of étale Z_p-local systems on algebraic varieties over non-closed fields are often non-zero even rationally. In particular, if X is a smooth variety over a p-adic field, and the local system is de Rham, then its characteristic classes are related to Chern classes of the graded quotients of the Hodge filtration on the associated vector bundle with connection. This relation can be established through considering an analog of Chern classes for vector bundles on the pro-étale site of X. This is a joint work with Lue Pan.
2024-04-25T00:00:00+02:00
Alexander Petrov
p-adic Hodge theory, local systems, characteristic classes, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-6c56e2151f537f841d49a87e1c8789a7.jpg
oai:carmin.tv:vanishing-theorems-for-the-irregular-hodge-filtration
2024-04-25T16:12:01+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:vanishing-theorems-for-the-irregular-hodge-filtration
https://www.carmin.tv/fr/video/vanishing-theorems-for-the-irregular-hodge-filtration
Vanishing Theorems for the Irregular Hodge Filtration
video/mp4
IHES
I will give an overview of recent advances concerning the irregular Hodge filtration (introduced by Deligne 40 years ago) and I will focus on Kodaira vanishing theorems similar to those of Saito for mixed Hodge modules.
2024-04-24T00:00:00+02:00
Claude Sabbah
Irregular Hodge theory, irregular Hodge filtration, vanishing theorems, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-545b2897c72afd9e56b3863781bb8093.jpg
oai:carmin.tv:the-non-abelian-p-curvature-conjecture
2024-04-25T16:12:01+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:the-non-abelian-p-curvature-conjecture
https://www.carmin.tv/fr/video/the-non-abelian-p-curvature-conjecture
The Non-Abelian p-Curvature Conjecture
video/mp4
IHES
The classical Grothendieck-Katz p-curvature conjecture gives an arithmetic criterion for the solutions to an algebraic linear ODE to be algebraic functions. We formulate a version of the p-curvature conjecture for certain non-linear ODEs arising from algebraic geometry (for example, the Painlevé VI equation or the Schlesinger system), which implies the classical conjecture, and prove it for "Picard-Fuchs initial conditions." The proof is inspired in part by Katz's resolution of the classical p-curvature conjecture for Picard-Fuchs equations, and in part by Esnault-Groechenig's recent resolution of the classical conjecture for rigid Z-local systems. This is joint work with Josh Lam.
2024-04-24T00:00:00+02:00
Daniel Litt
Arithmetic geometry, p-curvature conjecture, isomonodromy, non-abelian Hodge theory, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-25d905b88e9909a2935160921555d097.jpg
oai:carmin.tv:motives-and-super-representation-theory-principles-and-case-studies
2024-04-25T16:12:01+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:motives-and-super-representation-theory-principles-and-case-studies
https://www.carmin.tv/fr/video/motives-and-super-representation-theory-principles-and-case-studies
Motives and (super-)representation theory: principles and case studies
video/mp4
IHES
I shall outline how existence and shape of motives can sometimes be (not only predicted but) established using abstract motivic Galois theory, bypassing concrete constructions of algebraic cycles.
2024-04-24T00:00:00+02:00
Yves André
Motive, Super-representations, sign conjecture, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-2943e033151d6ac70233b7dcce197073.jpg
oai:carmin.tv:characteristic-cycle-and-pushforward
2024-04-25T16:10:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:characteristic-cycle-and-pushforward
https://www.carmin.tv/fr/video/characteristic-cycle-and-pushforward
Characteristic Cycle and Pushforward
video/mp4
IHES
Characteristic cycle for l-adic sheaf was introduced by T. Saito after the existence of singular support by Beilinson. This measures the ramification of the sheaf, and can be viewed as a vast generalization of Swan conductor. Various compatibility with cohomological operation had been verified by Saito and Beilinson, but the compatibility of pushforward along proper morphism has been left open. In this talk, I wish to discuss this compatibility.
2024-04-23T00:00:00+02:00
Tomoyuki Abe
characteristic cycle, Ramification theory, l-adic sheaf, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-259d9098bf98d18be4703babce710479.jpg
oai:carmin.tv:the-bloch-esnault-kerz-fiber-square
2024-04-24T15:20:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:the-bloch-esnault-kerz-fiber-square
https://www.carmin.tv/fr/video/the-bloch-esnault-kerz-fiber-square
The Bloch-Esnault-Kerz fiber square
video/mp4
IHES
A theorem of Bloch-Esnault-Kerz published in 2014 states that the formal part of the Fontaine-Messing $p$-adic variational Hodge conjecture holds for schemes smooth and proper over an unramified local number ring. The theorem states that a class in the rational $p$-adic Grothendieck group of the special fiber admits a lifting to the rational $p$-adic continuous Grothendieck group of the formal completion along the special fiber if and only if the image of its crystalline Chern class under the de Rham-crystalline comparison isomorphism lies in the appropriate part of the Hodge filtration. In a paper also published in 2014, Beilinson generalized the equivalence of the relative rational $p$-adic $K$-theory and cyclic homology, implicit in the Bloch-Esnault-Kerz paper. As much else, this work, was greatly clarified by the Bhatt-Morrow-Scholze unification of $p$-adic Hodge theory and topological cyclic. Indeed, Antieau-Mathew-Morrow-Nikolaus showed that Beilinson's equivalence is given by the map of horizontal fibers in a square in which the map of vertical fibers is an equivalence by the Nikolaus-Scholze Tate-Orbit-Lemma. In this talk, I will recall how said cartesian square appears from the Nikolaus-Scholze Frobenius of $\mathbb{Z}$ and explain a proposal by Clausen for how it may lead to a definition of the Hodge-Tate period map that does not require any calculational input.
2024-04-23T00:00:00+02:00
Lars Hesselholt
topological Hochschild homology, Hodge-Tate period map, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-965cb77b62f8799bda26e3af2651cd1d.jpg
oai:carmin.tv:on-secondary-invariants-and-arithmetic-rigidity
2024-04-24T15:20:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:on-secondary-invariants-and-arithmetic-rigidity
https://www.carmin.tv/fr/video/on-secondary-invariants-and-arithmetic-rigidity
On Secondary Invariants and Arithmetic Rigidity
video/mp4
IHES
A complex local system on a space S gives rise to "secondary" Chern classes in $H^{2p-1}(S;C/Z(p))$, refining the usual "primary" Chern classes in $H^{2p}(S;Z(p))$. In fact, Esnault in a survey article describes four methods of defining such classes, of which 3 are proved to be equivalent by means of her "modified splitting principle". I will explain how to show that the remaining 1 out of 4 definitions, that of Cheeger-Simons, agrees with the others. Then, changing gears, I will describe some arithmetic analogs of the phenomenon of rigidity of secondary Chern classes. This has bearing on another question from Esnault's article, and leads us to some motivic speculations.
2024-04-23T00:00:00+02:00
Dustin Clausen
local systems, Secondary characteristic classes, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-bf95c7ccdb36c911a7eb483facddcb35.jpg
oai:carmin.tv:finiteness-questions-for-etale-coverings-with-bounded-wild-ramification-at-the-boundary
2024-04-24T15:22:01+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:finiteness-questions-for-etale-coverings-with-bounded-wild-ramification-at-the-boundary
https://www.carmin.tv/fr/video/finiteness-questions-for-etale-coverings-with-bounded-wild-ramification-at-the-boundary
Finiteness Questions for Étale Coverings with Bounded Wild Ramification at the Boundary
video/mp4
IHES
We will consider étale coverings $ f : Y {\rightarrow} X$ of varieties over an algebraically closed field in characteristic p > 0 (with some further restrictions on the boundary ramification, in the non-proper case). This talk will give an overview of some work done with Hélène Esnault and others over the last few years, as well as open problems, related to this theme.
2024-04-23T00:00:00+02:00
Vasudevan Srinivas
étale coverings, bounded wild ramification, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-edbe455b606eab8952a978e08258f77c.jpg
oai:carmin.tv:donaldson-thomas-invariants-classical-motivic-quadratic-and-real
2024-04-24T15:22:01+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:donaldson-thomas-invariants-classical-motivic-quadratic-and-real
https://www.carmin.tv/fr/video/donaldson-thomas-invariants-classical-motivic-quadratic-and-real
Donaldson-Thomas Invariants: Classical, Motivic, Quadratic and Real
video/mp4
IHES
Let X be a smooth projective 3-fold over the complex numbers. Following work of Thomas, Behrend-Fantechi, and others, one has a virtual fundamental class in the Chow group of 0-cycles on the Hilbert scheme of dimension 0, length n subschemes of X, the degree of which is the nth Donaldson-Thomas invariant of X.
Now take X over an arbitrary field k. We have developed a construction of virtual fundamental classes with values in an arbitrary motivic cohomology theory. An example of such, a ``quadratic'' analog of the Chow groups, is the cohomology of the sheaf of Witt rings, which leads to a refinement of the classical DT-invariants to quadratic DT-invariants with values in the Witt ring of quadratic forms over k. We will discuss some developments and conjectures for these refined DT invariants, including some computations of the signature of these invariants due to Anneloes Viergever.
2024-04-23T00:00:00+02:00
Marc Levine
quadratic forms, Donaldson-Thomas invariants, enumerative geometry, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-10548b056975aead521a955a40ac942e.jpg
oai:carmin.tv:positive-mass-theorem-for-asymptotically-flat-manifolds-with-isolated-conical-singularities
2024-04-24T19:46:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:positive-mass-theorem-for-asymptotically-flat-manifolds-with-isolated-conical-singularities
https://www.carmin.tv/fr/video/positive-mass-theorem-for-asymptotically-flat-manifolds-with-isolated-conical-singularities
Positive mass theorem for asymptotically flat manifolds with isolated conical singularities
video/mp4
IHES
In this talk, I will mainly report recent joint works with Xianzhe Dai and Yukai Sun on positive mass theorem (PMT) for asymptotically flat (AF) manifolds with isolated conical singularities. In spin setting, we extend Witten’s argument by solving Dirac operator on AF manifolds with isolated conical singularities. In non-spin setting, we apply the conformal blow up technique and Hirsch-Miao’s PMT on AF manifolds with boundary. Here we solve Laplace equation on conically singular AF manifolds. For proving the rigidity result, we also need a partial asymptotical expansion for solutions. Moreover, with the help of these analysis on conically singular manifolds, by applying conformal blow up technique and Chodosh-Li’s and Wang-Zhang’s generalized Geroch type results on complete manifold, we prove a Geroch type result for isolated conical singularity.
2024-04-10T00:00:00+02:00
Changliang Wang
Researchers
en
https://www.carmin.tv/uploads/video/video-72d180aca61931cc1d9da096a159fbd1.jpg
oai:carmin.tv:positive-mass-theorem-and-positive-scalar-curvature-in-the-presence-of-a-singularity
2024-04-24T19:46:02+02:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:positive-mass-theorem-and-positive-scalar-curvature-in-the-presence-of-a-singularity
https://www.carmin.tv/fr/video/positive-mass-theorem-and-positive-scalar-curvature-in-the-presence-of-a-singularity
Positive mass theorem and positive scalar curvature in the presence of a singularity
video/mp4
IHES
The positive mass theorem of Schoen-Yau and Witten is one of the most important results about scalar curvature. It is intimately connected with the existence of positive scalar curvature metrics. Various motivations lead to consideration of singular metrics. In this talk I will survey some recent results of many people along this direction and present our recent work with Yukai Sun and Changliang Wang for isolated conical singularity.
2024-04-10T00:00:00+02:00
Xianzhe Dai
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-062bb2efc957a6f07ae7cf8cd9a945c4.jpg
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-2-4
2024-04-23T22:46:02+02:00
videos:institution:ihes
videos:collection:clement-delcamp-topological-symmetry-and-duality-in-quantum-lattice-models
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-2-4
https://www.carmin.tv/fr/video/topological-symmetry-and-duality-in-quantum-lattice-models-2-4
Topological Symmetry and Duality in Quantum Lattice Models (2/4)
video/mp4
IHES
A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.
2024-04-23T00:00:00+02:00
Clément Delcamp
, duality, Generalised symmetry, Topology, Lattice models, Researchers, Graduate Students
en
Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models / 16/04/2024 - 03/05/2024
https://www.carmin.tv/uploads/video/video-c24db86fbe382e155e0fe206639a059b.jpg
oai:carmin.tv:finite-type-properties-of-tame-fundamental-groups
2024-04-23T15:26:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:finite-type-properties-of-tame-fundamental-groups
https://www.carmin.tv/fr/video/finite-type-properties-of-tame-fundamental-groups
Finite Type Properties of (Tame) Fundamental Groups
video/mp4
IHES
We are interested in finite generation or finite presentation of fundamental groups as topological profinite groups. Our knowledge of group theoretic properties of étale fundamental groups relies traditionally on Riemann's existence theorem (in char 0) and Grothendieck's specialization map (for the transition to char p). But not all varieties lift to characteristic 0. Building on recent results by Esnault, Shusterman and Srinivas for smooth projective varieties in char p, we are going to explain in the talk how to generalize finite presentation to arbitrary proper varieties (joint work with Lara and Srinivas). Furthermore, we introduce an adic tameness condition and discuss finite generation/presentation of tame fundamental groups for rigid analytic spaces. The second part is joint work with Achinger, Lara and Hübner.
2024-04-22T00:00:00+02:00
Jakob Stix
positive characteristic, adic spaces, étale fundamental group, finite generation, finite presentation, tame ramification, tame topology, tame fundamental group, logarithmic geometry beyond fs, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-d955738b1da0f0ce5e6731081fc4fb1d.jpg
oai:carmin.tv:pure-local-systems-over-local-fields
2024-04-23T15:26:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:pure-local-systems-over-local-fields
https://www.carmin.tv/fr/video/pure-local-systems-over-local-fields
Pure Local Systems Over Local Fields
video/mp4
IHES
In joint work with Hélène we study certain pure l-adic local systems on varieties over p-adic local fields which are analogs of variations of pure Hodge structures. In the talk I will explain an approach via tilting to the most basic open problems in this setting: analogs of limiting mixed Hodge structures and purity of cohomology for a curve.
2024-04-22T00:00:00+02:00
Moritz Kerz
purity, local fields, local systems, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-e830900269732ff67dc8ff942f1eaf7d.jpg
oai:carmin.tv:various-remarks-on-the-donagi-pantev-program-for-construction-of-hecke-eigensheaves
2024-04-23T15:38:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:various-remarks-on-the-donagi-pantev-program-for-construction-of-hecke-eigensheaves
https://www.carmin.tv/fr/video/various-remarks-on-the-donagi-pantev-program-for-construction-of-hecke-eigensheaves
Various Remarks on the Donagi-Pantev Program for Construction of Hecke Eigensheaves
video/mp4
IHES
Donagi and Pantev set out a program for the construction of the parabolic logarithmic Higgs sheaves associated to Hecke eigensheaves in the geometric Langlands correspondence. One of the main features is that their spectral varieties over Bun_G are Hitchin fibers viewed birationally as subvarieties of T^*(Bun_G). We'll discuss various aspects of this construction: cases where it is known, the difficulties that can arise, and relationships with the geometry of the Hitchin moduli space.
2024-04-22T00:00:00+02:00
Carlos Simpson
Higgs bundle, moduli space, Local system, Geometric Langlands correspondence, Hecke eigensheaves, Spectral variety, Nonabelian Hodge theory, Hitchin morphism, Parabolic structure, Quadric line complex, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-5a85cb754caf461d93426438c6e551f5.jpg
oai:carmin.tv:different-notions-of-tameness-revisited
2024-04-23T15:38:02+02:00
videos:institution:ihes
videos:collection:arithmetic-geometry-a-conference-in-honor-of-helene-esnault-on-the-occasion-of-her-70th-birthday
oai:carmin.tv:different-notions-of-tameness-revisited
https://www.carmin.tv/fr/video/different-notions-of-tameness-revisited
Different Notions of Tameness Revisited
video/mp4
IHES
For an étale morphism $f:Y \to X$ of schemes over a base~$S$ there are different approaches to define what it means that~$f$ is tame. Behind all of them lies the intuition that the induced morphism of compactifications $\bar{f} : \bar{Y} \to \bar{X}$ is tamely ramified along the boundary $\bar{Y} \setminus Y$ (in an appropriate sense). Many of the tameness definitions work with valuations without relying on the choice of a compactification. Kerz and Schmidt compare these different notions of tameness in their article \emph{On different notions of tameness} mainly working with compactifications. The disadvantage of this approach is that they need to assume resolution of singularities in order to obtain nice compactifications. In my talk I want to present work in progress with Michael Temkin that approaches the problem purely valuation theoretic by using nonachimedean geometry. As a consequence we can drop the assumption on resolution of singularities. The heart of the project lies in a careful study of the geometry of adic curves over an arbitrary affinoid field (of higher rank) and of the wild locus of an étale morphism of such curves.
2024-04-22T00:00:00+02:00
Katharina Hübner
non-Archimedean geometry, wild ramification, adic curves, local uniformization, Researchers, Graduate Students
en
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday / This conference centers around the mathematical contributions and interests of Hélène Esnault. It aims at bringing together mathematicians with diverse backgrounds, providing a platform to exchange their ideas and foster new collaborations. / Marco D'Addezio, Kay Rülling, Tanya Srivastava / 22/04/2024 - 26/04/2024 / https://indico.math.cnrs.fr/event/11114/
https://www.carmin.tv/uploads/video/video-6b1bb6d07ccc0c471ef37a86cb221a44.jpg
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-1-4
2024-04-17T17:28:02+02:00
videos:institution:ihes
videos:collection:clement-delcamp-topological-symmetry-and-duality-in-quantum-lattice-models
oai:carmin.tv:topological-symmetry-and-duality-in-quantum-lattice-models-1-4
https://www.carmin.tv/fr/video/topological-symmetry-and-duality-in-quantum-lattice-models-1-4
Topological Symmetry and Duality in Quantum Lattice Models (¼)
video/mp4
IHES
A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.
2024-04-16T00:00:00+02:00
Clément Delcamp
, duality, Generalised symmetry, Topology, Lattice models, Researchers, Graduate Students
en
Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models / 16/04/2024 - 03/05/2024
https://www.carmin.tv/uploads/video/video-3401b23cf2d504e5821fa8140ba8131a.jpg
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-4-4
2024-04-16T20:46:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-4-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-4-4
Beauty of Life seen through Keyhole of Mathematics (4/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-16T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-f8607a03d9ec03afc23fdd44d096ad36.jpg
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-3-4
2024-04-10T16:46:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-3-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-3-4
Beauty of Life seen through Keyhole of Mathematics (3/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-09T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-fb4d39da39e960fc6bb3b8378361f4b4.jpg
oai:carmin.tv:reinforcement-learning-an-introduction-and-some-results-1
2024-04-09T19:40:18+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:reinforcement-learning-an-introduction-and-some-results-1
https://www.carmin.tv/fr/video/reinforcement-learning-an-introduction-and-some-results-1
Reinforcement Learning, an Introduction and Some Results
video/mp4
IHES
Reinforcement Learning is the "art" of learning how to act in an environment that is only observed through interactions.
In this talk, I will provide an introduction to this topic starting from the underlying probabilistic model, Markov Decision Process, describing how to learn a good policy (how to pick the actions) when this model is known and when it is unknown. I will stress the impact of the (required) parametrization of the solution, as well as the importance of understanding the inner engine (stochastic approximation).
I will illustrate the variety of questions by describing briefly three different questions:
- How to apply Reinforcement Learning to detect faster an issue during an ultrasound exam ?
- How to solve faster an MDP using better approximation ?
- How to make RL more robust while controlling its sample complexity ?
2024-04-03T00:00:00+02:00
Erwan Le Pennec
reinforcement learning, Stochastic approximation, Robust Reinforcement Learning, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-32097e08f4b8a99fa8b5c5762b9885e2.jpg
oai:carmin.tv:contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
2024-04-09T19:42:20+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
https://www.carmin.tv/fr/video/contextual-stochastic-bandits-with-budget-constraints-and-fairness-application-1
Contextual Stochastic Bandits with Budget Constraints and Fairness Application
video/mp4
IHES
We review the setting and fundamental results of contextual stochastic bandits, where at each round some vector-valued context $x_t$ is observed and $K$ actions are available, each action a providing a stochastic reward with expectation given by some (partially unknown) function of $x_t$ and $a$. The aim is to maximize the cumulative rewards obtained, or equivalently, to minimize the regret. This requires maintaining a good balance between the estimation (a.k.a., exploration) of the function and the exploitation of the estimates built. The literature also considers additional budget constraints (leading to so-called contextual bandits with knapsacks): actions now provide rewards but also costs. The literature also illustrated that costs may model fairness constraints. We will review these two lines of work and briefly describe our own contribution in this respect, related to a more direct strategy, able to handle $\sqrt{T}$ cost constraints over $T$ rounds, which is exactly what is needed for fairness applications. The recent results discussed at the end of the talk will be based on the joint work by Evgenii Chzhen, Christophe Giraud, Zhen Li, and Gilles Stoltz, Small total-cost constraints in contextual bandits with knapsacks, with application to fairness, Neurips, 2023.
2024-04-03T00:00:00+02:00
Gilles Stoltz
Contextual bandits with Knapsacks, Algorithmic fairness, Adaptive stochastic optimization, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-60db1d207aafdd88f89bd2bfcba351e0.jpg
oai:carmin.tv:unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
2024-04-09T19:41:21+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
https://www.carmin.tv/fr/video/unsupervised-alignment-of-graphs-and-embeddings-fundamental-limits-and-computational-methods-1
Unsupervised Alignment of Graphs and Embeddings: Fundamental Limits and Computational Methods
video/mp4
IHES
Aligning two (weighted or unweighted) graphs, or matching two clouds of high-dimensional embeddings, are fundamental problems in machine learning with applications across diverse domains such as natural language processing to computational biology. In this presentation I will introduce the graph alignment problem, which can be viewed as an average-case and noisy version of the graph isomorphism problem. I will talk about the main challenges when the graphs are sparse, give some insights on the fundamental limits, and present efficient algorithms for this task. Then, switching focus on aligning clouds of embeddings, I will delve into the Procrustes-Wassertein problem. We will emphasize differences from the previous graph-to-graph case. Statistical and computational results will be presented to shed light on these emerging questions.
2024-04-03T00:00:00+02:00
Luca Ganassali
Statistical inference in graphs and matrices, Informational and computational thresholds for algorithms on random instances, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-d5ac6d25b2c930a83bf2e8bc8f3dab3d.jpg
oai:carmin.tv:learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
2024-04-09T19:40:46+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
https://www.carmin.tv/fr/video/learning-with-missing-values-theoretical-insights-and-application-to-health-databases-1
Learning with Missing Values: Theoretical Insights and Application to Health Databases
video/mp4
IHES
Missing values are ubiquitous in many fields such as health, business or social sciences. To date, much of the literature on missing values has focused on imputation as well as inference with incomplete data. In contrast, supervised learning in the presence of missing values has received little attention. In this talk I will explain the challenges posed by missing values in regression and classification tasks. In practice, a common solution consists in imputing the missing values prior to learning. I will show how different baseline methods for handling missing values compare on several large health databases with naturally occurring missing values. We will then examine the theoretical foundations of Impute-then-Regress approaches. Finally, I will present a neural network architecture for learning with missing values that goes beyond the two-stage Impute-then-Regress approaches.
2024-04-03T00:00:00+02:00
Marine Le Morvan
Inference with missing data, Machine learning for health domain, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-1e4df2c4ca4afa53cac42fd89a6cc7d6.jpg
oai:carmin.tv:weak-signals-machine-learning-meets-extreme-value-theory-1
2024-04-09T19:41:53+02:00
videos:institution:ihes
videos:collection:9e-journee-statistique-et-informatique-pour-la-science-des-donnees-a-paris-saclay
oai:carmin.tv:weak-signals-machine-learning-meets-extreme-value-theory-1
https://www.carmin.tv/fr/video/weak-signals-machine-learning-meets-extreme-value-theory-1
Weak Signals: machine-learning meets extreme value theory
video/mp4
IHES
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In the common situation that the components of the vector have different distributions, the rank transformation offers a convenient and robust way of standardizing data in order to build an empirical version of the angular measure based on the most extreme observations. However, the study of the sampling distribution of the resulting empirical angular measure is challenging. It is the purpose of this talk to explain how to establish finite-sample bounds for the maximal deviations between the empirical and true angular measures, uniformly over classes of Borel sets of controlled combi natorial complexity. The bounds are valid with high probability and, up to logarithmic factors, scale as the square root of the effective sample size. The bounds are next applied to provide performance guarantees for two statistical learning procedures tailored to extreme regions of the input space and built upon the empirical angular measure: binary classification in extreme regions through empirical risk minimization and unsupervised anomaly detection through minimum-volume sets of the sphere.
2024-04-03T00:00:00+02:00
Stephan Clémençon
extreme value theory, VC theory, empirical processes, Anomaly Detection, Researchers
en
9e Journée Statistique et Informatique pour la Science des Données à Paris-Saclay / The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers. / Evgenii Chzhen, Florence Tupin / 03/04/2024 - 03/04/2024 / https://indico.math.cnrs.fr/event/11698/
https://www.carmin.tv/uploads/video/video-44cfb67734dd90881c880a17d1ee0853.jpg
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-2-4
2024-04-02T21:26:02+02:00
videos:institution:ihes
videos:collection:misha-gromov-beauty-of-life-seen-through-keyhole-of-mathematics
oai:carmin.tv:beauty-of-life-seen-through-keyhole-of-mathematics-2-4
https://www.carmin.tv/fr/video/beauty-of-life-seen-through-keyhole-of-mathematics-2-4
Beauty of Life seen through Keyhole of Mathematics (2/4)
video/mp4
IHES
We start with reminding basic molecular structures (Crick dogma, genetic code etc.) in living entities and classical examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy on the nature of Life.
Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current and projected numerical data on the human role in ecology of Earth.
2024-04-02T00:00:00+02:00
Misha Gromov
life, bioengineering, Researchers, Graduate Students
en
Misha Gromov : Beauty of Life seen through Keyhole of Mathematics / 19/03/2024 - 16/04/2024
https://www.carmin.tv/uploads/video/video-b17141e76b968f541a3282f83520484f.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
2024-04-01T13:06:02+02:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-4-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (4/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-29T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-b1c060c60d2f46ef61e7e6d8c8ceb766.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
2024-03-27T22:36:03+01:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-3-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (3/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-27T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-d6f837a4b5a2ebe847fa392ee3941392.jpg
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
2024-03-25T20:16:02+01:00
videos:institution:ihes
videos:collection:gerard-ben-arous-random-matrices-and-dynamics-of-optimization-in-very-high-dimensions
oai:carmin.tv:random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
https://www.carmin.tv/fr/video/random-matrices-and-dynamics-of-optimization-in-very-high-dimensions-1-4
Random Matrices and Dynamics of Optimization in Very High Dimensions (1/4)
video/mp4
IHES
Machine learning and Data science algorithms involve in their last stage the need for optimization of complex random functions in very high dimensions. Simple algorithms like Stochastic Gradient Descent (with small batches) are used very effectively. I will concentrate on trying to understand why these simple tools can still work in these complex and very over-parametrized regimes. I will first introduce the whole framework for non-experts, from the structure of the typical tasks to the natural structures of neural nets used in standard contexts. l will then cover briefly the classical and usual context of SGD in finite dimensions. I will then survey recent work with Reza Gheissari (Northwestern), Aukosh Jagannath (Waterloo) giving a general view for the existence of projected “effective dynamics” for “summary statistics” in much smaller dimensions, which still rule the performance of very high dimensional systems, as well . These effective dynamics (as their so-called “critical regime”) define a dynamical system in finite dimensions which may be quite complex, and rules the performance of the learning algorithm. The next step will be to understand how the system finds these “summary statistics”. This is done in the next work with the same authors and with Jiaoyang Huang (Wharton, U-Penn). This is based on a dynamical spectral transition of Random Matrix Theory: along the trajectory of the optimization path, the Gram matix or the Hessian matrix develop outliers which carry these effective dynamics. I will naturally first come back to the Random Matrix Tools needed here (the behavior of the edge of the spectrum and the BBP transition) in a much broader context. And then illustrate the use of this point of view on a few central examples of ML: multilayer neural nets for classification (of Gaussian mixtures), and the XOR examples, for instance.
2024-03-25T00:00:00+01:00
Gérard Ben Arous
machine learning, random matrices, stochastic gradient descent, Optimization in high dimensions, Neural Nets, Researchers, Graduate Students
en
Gérard Ben Arous : Random Matrices and Dynamics of Optimization in Very High Dimensions / 25/03/2024 - 29/03/2024
https://www.carmin.tv/uploads/video/video-457dc4d80a61efc335d77c163cc83804.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-3-4
2024-03-15T20:44:01+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-3-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-3-4
An Introduction to Super Critical Singularities (3/4)
video/mp4
IHES
Lecture 3 : On self similar solutions for compressible Euler
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-15T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-4e1c7801935140fc80814395f536b612.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-2-4
2024-03-14T19:20:02+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-2-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-2-4
An Introduction to Super Critical Singularities (2/4)
video/mp4
IHES
Lecture 2 : Front singularities
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-14T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-553beed0edfbc69c5b782f36c3a88db5.jpg
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-2
2024-03-13T10:08:02+01:00
videos:institution:ihes
videos:collection:jonathan-pila-point-counting-and-the-zilber-pink-conjecture
oai:carmin.tv:point-counting-and-the-zilber-pink-conjecture-4-4-2
https://www.carmin.tv/fr/video/point-counting-and-the-zilber-pink-conjecture-4-4-2
Point-Counting and the Zilber-Pink Conjecture (4/4)
video/mp4
IHES
The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.
2024-03-12T00:00:00+01:00
Jonathan Pila
Zilber-Pink conjecture, unlikely intersection, o-minimal structure, Researchers, Graduate Students
en
Jonathan Pila : Point-Counting and the Zilber-Pink Conjecture / 20/02/2024 - 12/03/2024
https://www.carmin.tv/uploads/video/video-5d1a3ca93ad33c9ca0aba915e0c86183.jpg
oai:carmin.tv:an-introduction-to-super-critical-singularities-1-4
2024-03-13T10:48:01+01:00
videos:institution:ihes
videos:collection:pierre-raphael-une-introduction-aux-singularites-sur-critiques
oai:carmin.tv:an-introduction-to-super-critical-singularities-1-4
https://www.carmin.tv/fr/video/an-introduction-to-super-critical-singularities-1-4
An Introduction to Super Critical Singularities (1/4)
video/mp4
IHES
Lecture 1 : Energy super critical singularity formation
The description of singularity formation for non linear PDE’s is a classical problem with deep physical roots. Immense progress have been done in the last thirty on the understanding of “bubbling” phenomenon for focusing problems. But recently, new mecanisms have been discovered for “defocusing” problems with a deep connection to fluid mechanics. This series of 4 lectures is intended as a graduate class and will propose an introduction to the key results and open problems in the field, as well as a self contained description of the essential steps of the proofs.
2024-03-12T00:00:00+01:00
Pierre Raphaël
Researchers, Graduate Students
en
Pierre Raphael : Une introduction aux singularités sur critiques / 12/03/2024 - 19/03/2024
https://www.carmin.tv/uploads/video/video-8168f3d71c21cd627f6fab1e84528268.jpg
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
2024-03-12T16:06:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
https://www.carmin.tv/fr/video/particle-approximation-of-the-doubly-parabolic-keller-segel-equation-in-the-plane-1
Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
video/mp4
IHES
In this talk, we study a stochastic system of $N$ particles associated with the parabolic-parabolic Keller-Segel system in the plane. This particle system is singular and non Markovian in that its drift term depends on the past of the particles. When the sensitivity parameter is sufficiently small, we show that this particle system indeed exists for any $N\geq 2$, we show tightness in $N$ of its empirical measure, and that any weak limit point of this empirical measure, as $N\to \infty$, solves some nonlinear martingale problem, which in particular implies that its family of time-marginals solves the parabolic-parabolic Keller-Segel system in some weak sense. The main argument of the proof consists of a "Markovianization" of the interaction kernel: We show that, in some loose sense, the two-by-two path-dependant interaction can be controlled by a two-by-two Coulomb interaction, as in the parabolic-elliptic case. This is a joint work with N. Fournier (Sorbonne Université).
2024-03-08T00:00:00+01:00
Milica Tomašević
Stochastic particle systems, Singular interaction, Non-Markovian processes, Keller-Segel equation, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-e9b9c690e4b688c00297e4f4b1d118c0.jpg
oai:carmin.tv:scaling-limits-of-disordered-systems-1
2024-03-12T16:12:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:scaling-limits-of-disordered-systems-1
https://www.carmin.tv/fr/video/scaling-limits-of-disordered-systems-1
Scaling Limits of Disordered Systems
video/mp4
IHES
I will present some recent results on the scaling limit of disordered systems and some of their consequences. I will mostly focus on the PolandâScheraga model, also known as the pinning model, which is used to describe DNA denaturation: the question is to know wether (and how) disorder affects its phase transition. I will present some results obtained in a generalized (supposedly more realistic) version of the model, in collaboration with Alexandre Legrand (Université Lyon 1).
2024-03-08T00:00:00+01:00
Quentin Berger
disordered systems, critical phenomena, scaling limits, intermediate disorder, disorder relevance, correlated disorder, Poland–Scheraga model, bivariate renewal processes, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-b1fb153a1d35a3cd28bf36167693368e.jpg
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
2024-03-12T16:14:02+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
https://www.carmin.tv/fr/video/equivalence-of-fluctuations-between-she-and-kpz-equation-in-weak-disorder-regime-1
Equivalence of Fluctuations Between SHE and KPZ Equation in Weak Disorder Regime
video/mp4
IHES
I will The Kardar-Parisi-Zhang (KPZ) equation is a mathematical model that describes the random evolution of interfaces. The equation has become a fundamental model in non-equilibrium statistical physics. Constructing a solution to the KPZ equation in any dimension presents a significant challenge due to its inherent non-linearity. This challenge has resulted in an enduring open problem, particularly in finding solutions in two and higher dimensions. This talk will explore the intriguing connection between the stochastic heat equation (SHE) and the KPZ equation. It offers a rigorous demonstration of the equivalence of fluctuations in these systems in the weak disorder regime for three and higher dimensions. This talk is based on joint work with Stefan Junk (Gakushuin University).
2024-03-08T00:00:00+01:00
Shuta Nakajima
KPZ equation, directed polymer, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-6d30a250e19311b1aa38d105c2110e3e.jpg
oai:carmin.tv:where-do-random-trees-grow-leaves-1
2024-03-12T16:16:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:where-do-random-trees-grow-leaves-1
https://www.carmin.tv/fr/video/where-do-random-trees-grow-leaves-1
Where Do Random Trees Grow Leaves
video/mp4
IHES
Luczak and Winkler (refined by Caraceni and Stauffer) showed that is it possible to create a chain of random binary trees $(T_n : n \geq 1)$ so that $T_{n}$ is uniformly distributed over the set of all binary trees with $n$ leaves and such that $T_{n+1}$ is obtained from $T_{n}$ by adding "on leaf". We show that the location where this leaf must be added is far from being uniformly distributed on $T_n$ but is concentrated on a "fractal" subset of $n^{3(2- \sqrt{3})+o(1)}$ leaves. The full multifractal spectrum of the measure in the continuous setting is computed. Joint work with Alessandra Caraceni and Robin Stephenson.
2024-03-08T00:00:00+01:00
Nicolas Curien
random trees, scaling limits, Markov dynamic, fractal measure, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-eb5fcc25f4345ef859b1039a43d0576a.jpg
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
2024-03-12T16:16:01+01:00
videos:institution:ihes
videos:collection:french-japanese-conference-on-probability-and-interactions
oai:carmin.tv:geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
https://www.carmin.tv/fr/video/geometric-laplacians-on-self-conformal-fractal-curves-in-the-plane-1
Geometric Laplacians on Self-Conformal Fractal Curves in the Plane
video/mp4
IHES
This talk will present the speaker's ongoing work on “geometrically canonical” Laplacians on self-conformal fractal curves in the plane. The main result is that on a given such curve one can construct a family of Laplacians whose heat kernels and eigenvalue asymptotics “respect” the fractal nature of the Euclidean geometry of the curve in certain nice ways. The idea of the construction of such Laplacians originated from the speaker's preceding studies on the case of a circle packing fractal, i.e., a fractal subset of $\mathbb{C}$ whose Lebesgue area is zero and whose complement in the Riemann sphere $\widehat{\mathbb{C}}:=\mathbb{C}\cup\{\infty\}$ is the union of disjoint open disks in $\widehat{\mathbb{C}}$. He has observed that, on a given such fractal, one can explicitly define a Dirichlet form (a quadratic energy functional) by a certain weighted sum of the standard one-dimensional Dirichlet form on each of the circles constituting the fractal, and that this Dirichlet form “respect” the Euclidean geometry of the fractal in the sense that the inclusion map of the fractal into $\mathbb{C}$ is harmonic with respect to this form. The speaker has also proved that such a Dirichlet form is unique for the classical Apollonian gaskets and that, for some concrete families of self-conformal circle packing fractals including the Apollonian gaskets, the associated Laplacian satisfies Weyl's eigenvalue asymptotics involving the Euclidean Hausdorff dimension and measure of the fractal. It would be desirable if one could extend such results to self-conformal fractals which are not circle packing ones, and the talk will present an extension to the simplest case of self-conformal fractal curves in the plane. The key point of the construction of Laplacians is to use (suitable versions of) the harmonic measure in defining the Dirichlet form BUT to use fractional-order Besov seminorms (with respect to the harmonic measure) of the inclusion map into $\mathbb{C}$ in defining the $L^{2}$-inner product for functions on the fractal.
2024-03-08T00:00:00+01:00
Naotaka Kajino
harmonic measure, Laplacian, self-conformal fractal curve, Apollonian gasket, round Sierpinski carpet, Weyl’s eigenvalue asymptotics, Kesten's renewal theorem, Researchers, Graduate Students
en
French Japanese Conference on Probability and Interactions / The conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries. / Anne de Bouard, Thierry Bodineau, Reika Fukuizumi / 06/03/2024 - 08/03/2024 / https://indico.math.cnrs.fr/event/10598/
https://www.carmin.tv/uploads/video/video-5d9e19841bf7afcf1ac930bb3692dcd8.jpg
eyJwYWdlIjoxLCJzZXQiOiJ2aWRlb3M6aW5zdGl0dXRpb246aWhlcyIsIm1ldGFkYXRhUHJlZml4Ijoib2FpX2RjIn0=