2023-03-25T20:52:43+01:00
https://www.carmin.tv/fr/oai
oai:carmin.tv:les-sept-filles-deve
2023-03-24T17:04:01+01:00
videos:institution:ihes
videos:collection:les-amis-de-lihes-1
oai:carmin.tv:les-sept-filles-deve
https://www.carmin.tv/fr/video/les-sept-filles-deve
Les Sept Filles d’Eve
video/mp4
IHES
L’ADN mitochondrial est uniquement transmis par les mères. L’analyse des mutations successives a permis de démontrer que les européens descendent de 7 femmes (Les Sept Filles d’Eve de Brian Sykes), et que la population mondiale se structure en une quarantaine de lignées.
2023-03-14T00:00:00+01:00
Jacques-Deric Rouault
General Public
fr
Les amis de l’IHES / 14/03/2023 - 14/03/2023
https://www.carmin.tv/uploads/video/video-552fed06da2c430116b3e30429cee55c.jpg
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-4-4
2023-03-22T12:26:02+01:00
videos:institution:ihes
videos:collection:sylvia-serfaty-systems-with-coulomb-interactions
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-4-4
https://www.carmin.tv/fr/video/systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-4-4
Systems with Coulomb Interactions : Mean-Field Limits and Statistical Mechanics (4/4)
video/mp4
IHES
We will discuss large systems of particles with Coulomb-type repulsion. The first part of the course will mention the question of mean-field for the dynamics of such systems via a modulated energy approach. The second part will be more expanded and concern the statistical mechanics of such systems (expansion of free energy, LDP for empirical field, fluctuations around the mean-field limit). Several tools and ideas are common to both parts.
2023-03-21T00:00:00+01:00
Mandarine Audiovisuel
Sylvia Serfaty
Researchers, Graduate Students
en
Sylvia Serfaty : Systems with Coulomb Interactions / 16/03/2023 - 21/03/2023
https://www.carmin.tv/uploads/video/video-8bb27ca875a9c67b03d550bcd8f5e3f2.jpg
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-3-4
2023-03-20T22:32:03+01:00
videos:institution:ihes
videos:collection:sylvia-serfaty-systems-with-coulomb-interactions
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-3-4
https://www.carmin.tv/fr/video/systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-3-4
Systems with Coulomb Interactions : Mean-Field Limits and Statistical Mechanics (3/4)
video/mp4
IHES
We will discuss large systems of particles with Coulomb-type repulsion. The first part of the course will mention the question of mean-field for the dynamics of such systems via a modulated energy approach. The second part will be more expanded and concern the statistical mechanics of such systems (expansion of free energy, LDP for empirical field, fluctuations around the mean-field limit). Several tools and ideas are common to both parts.
2023-03-20T00:00:00+01:00
Mandarine Audiovisuel
Sylvia Serfaty
Researchers, Graduate Students
en
Sylvia Serfaty : Systems with Coulomb Interactions / 16/03/2023 - 21/03/2023
https://www.carmin.tv/uploads/video/video-31fc3607ab4c46844800cb8e77a5b089.jpg
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-2-4
2023-03-17T21:48:02+01:00
videos:institution:ihes
videos:collection:sylvia-serfaty-systems-with-coulomb-interactions
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-2-4
https://www.carmin.tv/fr/video/systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-2-4
Systems with Coulomb Interactions : Mean-Field Limits and Statistical Mechanics (2/4)
video/mp4
IHES
We will discuss large systems of particles with Coulomb-type repulsion. The first part of the course will mention the question of mean-field for the dynamics of such systems via a modulated energy approach. The second part will be more expanded and concern the statistical mechanics of such systems (expansion of free energy, LDP for empirical field, fluctuations around the mean-field limit). Several tools and ideas are common to both parts.
2023-03-17T00:00:00+01:00
Mandarine Audiovisuel
Sylvia Serfaty
Researchers, Graduate Students
en
Sylvia Serfaty : Systems with Coulomb Interactions / 16/03/2023 - 21/03/2023
https://www.carmin.tv/uploads/video/video-86eee541ecfc7fa338d2558e13a0c427.jpg
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-1-4
2023-03-17T00:10:01+01:00
videos:institution:ihes
videos:collection:sylvia-serfaty-systems-with-coulomb-interactions
oai:carmin.tv:systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-1-4
https://www.carmin.tv/fr/video/systems-with-coulomb-interactions-mean-field-limits-and-statistical-mechanics-1-4
Systems with Coulomb Interactions : Mean-Field Limits and Statistical Mechanics (1/4)
video/mp4
IHES
We will discuss large systems of particles with Coulomb-type repulsion. The first part of the course will mention the question of mean-field for the dynamics of such systems via a modulated energy approach. The second part will be more expanded and concern the statistical mechanics of such systems (expansion of free energy, LDP for empirical field, fluctuations around the mean-field limit). Several tools and ideas are common to both parts.
2023-03-16T00:00:00+01:00
Mandarine Audiovisuel
Sylvia Serfaty
Researchers, Graduate Students
en
Sylvia Serfaty : Systems with Coulomb Interactions / 16/03/2023 - 21/03/2023
https://www.carmin.tv/uploads/video/video-4f29bf414e6e36eed912bf32df91f140.jpg
oai:carmin.tv:manifold-learning-with-noisy-data
2023-03-12T13:36:01+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:manifold-learning-with-noisy-data
https://www.carmin.tv/fr/video/manifold-learning-with-noisy-data
Manifold Learning with Noisy Data
video/mp4
IHES
It is a common idea that high dimensional data (or features) may lie on low dimensional support making learning easier. In this talk, I will present a very general set-up in which it is possible to recover low dimensional non-linear structures with noisy data, the noise being totally unknown and possibly large.
Then I will present minimax rates for the estimation of the support in Hausdorff distance.
2023-03-09T00:00:00+01:00
Elisabeth Gassiat
machine learning, mathematical statistics, deconvolution, Dimension Reduction, support estimation, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-c0825295c2580c568147a55cce7e18dc.jpg
oai:carmin.tv:hybrid-ai-for-knowledge-representation-and-model-based-image-understanding-towards-explainability
2023-03-12T13:40:01+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:hybrid-ai-for-knowledge-representation-and-model-based-image-understanding-towards-explainability
https://www.carmin.tv/fr/video/hybrid-ai-for-knowledge-representation-and-model-based-image-understanding-towards-explainability
Hybrid AI for Knowledge Representation and Model-based Image Understanding - Towards Explainability
video/mp4
IHES
This presentation will focus on hybrid AI, as a step towards explainability, more specifically in the domain of spatial reasoning and image understanding. Image understanding benefits from the modeling of knowledge about both the scene observed and the objects it contains as well as their relationships. We show in this context the contribution of hybrid artificial intelligence, combining different types of formalisms and methods, and combining knowledge with data. Knowledge representation may rely on symbolic and qualitative approaches, as well as semi-qualitative ones to account for their imprecision or vagueness.
Structural information can be modeled in several formalisms, such as graphs, ontologies, logical knowledge bases, or neural networks, on which reasoning will be based. Image understanding is then expressed as a problem of spatial reasoning. These approaches will be illustrated with examples in medical imaging, illustrating the usefulness of
combining several approaches.
2023-03-09T00:00:00+01:00
Isabelle Bloch
Hybrid and explainable AI, Knowledge Representation and Reasoning, Structural Models, Image Understanding, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-2de8d47fa0a3b4c418c8ffceee9b74ce.jpg
oai:carmin.tv:covariance-subspace-inference-handling-robustness-variability-and-incompleteness
2023-03-12T13:42:01+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:covariance-subspace-inference-handling-robustness-variability-and-incompleteness
https://www.carmin.tv/fr/video/covariance-subspace-inference-handling-robustness-variability-and-incompleteness
Covariance & Subspace Inference: Handling Robustness, Variability and Incompleteness
video/mp4
IHES
In this talk, we focus on covariance matrix inference and principal component analysis in the context of non-regular data under heterogeneous environments. First, we briefly introduce mixed effects models, which are widely used to analyze repeated measures data arising in several signal processing applications that need to incorporate the same global individual's behavior with possible local variations. Then, we will expose classical strategies to learn under Gaussian assumptions. It is worth mentioning that in certain situations, in which there exist outliers within the data set, the Gaussian assumption is not valid and leads to a dramatic performance loss. To overcome this drawback, we will present an expectation-maximization-based algorithm in which the heterogeneous component is considered part of the complete data. Then, the proposed algorithm is cast into a parallel scheme, w.r.t. the individuals, in order to alleviate the computational cost and a possible central processor overload. In addition, extensions to deal with missing data, which refers to the situation where part of the individual responses is unobserved, will be presented. Finally, applications related to calibration and imaging in the context of large radio-interferometers will be considered.
2023-03-09T00:00:00+01:00
Nabil El Korso
Expectation maximization algorithm, robustness, mixed effects models, missing data, radio interferometric calibration and imaging, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-02add44625f8fbb354db3a6f9648ead9.jpg
oai:carmin.tv:transfer-learning-covariant-learning-and-parallel-transport
2023-03-12T13:44:02+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:transfer-learning-covariant-learning-and-parallel-transport
https://www.carmin.tv/fr/video/transfer-learning-covariant-learning-and-parallel-transport
Transfer Learning, Covariant Learning and Parallel Transport
video/mp4
IHES
Transfer learning has become increasingly important in recent years, particularly because learning a new model for each task can be much more costly in terms of training examples than adapting a model learned for another task. The standard approach in neural networks is to reuse the learned representation in the first layers and to adapt the decision function performed by the last layers.
In this talk, we will revisit transfer learning. A dual algorithm of the standard approach, which adapts the representation while keeping the decision function, will be presented, as well as an algorithm for the early classification of time series. This will allow us to question the notion of bias in transfer learning as well as the cost of information and to ask ourselves which a priori assumptions are necessary to obtain guarantees on transfer learning.
We will note that reasoning by analogy and online learning are instances of transfer learning, and we will see how the notions of parallel transport and covariant physics can provide useful conceptual tools to address transfer learning.
2023-03-09T00:00:00+01:00
Antoine Cornuejols
transfer learning, Out Of Distribution learning, Parallel Transport, Learning Using Privileged Information, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-0cfeaac3e60b4b6c6ac10ef662d16d72.jpg
oai:carmin.tv:federated-learning-with-communication-constraints-challenges-in-compression-based-approaches
2023-03-12T13:26:02+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:federated-learning-with-communication-constraints-challenges-in-compression-based-approaches
https://www.carmin.tv/fr/video/federated-learning-with-communication-constraints-challenges-in-compression-based-approaches
Federated Learning with Communication Constraints: Challenges in Compression Based Approaches
video/mp4
IHES
In this presentation, I will present some results on optimization in the context of federated learning with compression. I will first summarise the main challenges and the type of results the community has obtained, and dive into some more recent results on tradeoffs between convergence and compression rates, and user-heterogeneity. In particular, I will describe two fundamental phenomenons (and related proof techniques): (1) how user-heterogeneity affects the convergence of federated optimization methods in the presence of communication constraints, and (2) the robustness of distributed stochastic algorithms to perturbation of the iterates, and the link with model compression. I will then introduce and discuss a new compression scheme based on random codebooks and unitary invariant distributions.
2023-03-09T00:00:00+01:00
Aymeric Dieuleveut
stochastic optimization, federated and collaborative learning, compression, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-03a2d96d2d733b6a028118cf035be6b0.jpg
oai:carmin.tv:leveraging-knowledge-to-design-machine-learning-despite-the-lack-of-industrial-data
2023-03-12T13:28:01+01:00
videos:institution:ihes
videos:collection:statistics-and-machine-learning-at-paris-saclay-2023-edition
oai:carmin.tv:leveraging-knowledge-to-design-machine-learning-despite-the-lack-of-industrial-data
https://www.carmin.tv/fr/video/leveraging-knowledge-to-design-machine-learning-despite-the-lack-of-industrial-data
Leveraging Knowledge to Design Machine Learning Despite the Lack of Industrial Data
video/mp4
IHES
In recent years, considerable progress has been made in the implementation of decision support procedures based on machine learning methods through the exploitation of very large databases and the use of learning algorithms.
In the industrial environment, the databases available in research and development or in production are rarely so voluminous and the question arises as to whether in this context it is reasonable to use machine learning methods.
This talk presents research work around transfer learning and hybrid models that use knowledge from related application domains or physics to implement efficient models with an economy of data.
Several achievements in industrial collaborations will be presented that successfully use these learning models to design machine learning for industrial small data regimes and to develop powerful decision support tools even in cases where the initial data volume is limited.
2023-03-09T00:00:00+01:00
Mathilde Mougeot
transfer learning, domain adaptation, adversarial learning, industrial applications, Researchers
en
Statistics and Machine Learning at Paris-Saclay (2023 Edition) / 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. / Gilles Blanchard, Florence Tupin / 09/03/2023 - 09/03/2023 / https://indico.math.cnrs.fr/event/9202/
https://www.carmin.tv/uploads/video/video-dfc95690fa02e38a0ee2356da6432182.jpg
oai:carmin.tv:from-twistors-to-gravitational-scattering-2-2
2023-03-10T14:37:00+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:from-twistors-to-gravitational-scattering-2-2
https://www.carmin.tv/fr/video/from-twistors-to-gravitational-scattering-2-2
From Twistors to Gravitational Scattering (2/2)
video/mp4
IHES
This lecture will obtain a compact twistor formula for the full tree-level gravitational S-matrix beyond the self-dual sector. It uses an extension of the complex geometry of twistor space of the previous lecture. In the final formula, all integrations are saturated against delta functions yielding a sum of residues. These depend on the n momenta and polarization vectors of associated gravity linear waves.
2023-03-08T00:00:00+01:00
Lionel Mason
scattering, Twistor, Gravity, Researchers
en
https://www.carmin.tv/uploads/video/video-91b99298e85f09f43b06cb28b6661dbd.jpg
oai:carmin.tv:from-twistors-to-gravitational-scattering-1-2
2023-03-07T10:56:24+01:00
videos:institution:ihes
videos:collection:balzan-lectures
oai:carmin.tv:from-twistors-to-gravitational-scattering-1-2
https://www.carmin.tv/fr/video/from-twistors-to-gravitational-scattering-1-2
From Twistors to Gravitational Scattering (1/2)
video/mp4
IHES
This lecture will review how linear gravity can be obtained from integral formulae from twistor space and how the fully nonlinear self dual sector of 4d gravity can be built using complex analysis. It will focus on global problems in split signature where the self-dual sector can be generated from a Hamiltonian deformation of the real slice of twistor space. The space-time is reconstructed from holomorphic discs in twistor space with boundary on the deformed real slice.
2023-03-01T00:00:00+01:00
Lionel Mason
scattering, Twistor, Gravity, Researchers
en
https://www.carmin.tv/uploads/video/video-dfe5be3c948dbd1c57e28d9e5478ca04.jpg
oai:carmin.tv:recent-developments-in-constant-mean-curvature-hypersurfaces-i
2023-02-21T10:36:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:recent-developments-in-constant-mean-curvature-hypersurfaces-i
https://www.carmin.tv/fr/video/recent-developments-in-constant-mean-curvature-hypersurfaces-i
Recent developments in constant mean curvature hypersurfaces I
video/mp4
IHES
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
2023-02-16T00:00:00+01:00
Xin Zhou
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-15ed12be9df7e9838ad00402be34bbcd.jpg
oai:carmin.tv:recent-developments-in-constant-mean-curvature-hypersurfaces-ii
2023-02-21T10:34:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:recent-developments-in-constant-mean-curvature-hypersurfaces-ii
https://www.carmin.tv/fr/video/recent-developments-in-constant-mean-curvature-hypersurfaces-ii
Recent developments in constant mean curvature hypersurfaces II
video/mp4
IHES
Continuing from the previous talk, we will first discuss two min-max theorems for constructing prescribed mean curvature hypersurfaces in non-compact spaces. The first concerns the existence of prescribed mean curvature hypersurfaces in Euclidean space, and the second concerns the existence of constant mean curvature hypersurfaces in asymptotically flat manifolds. Following this, we will introduce the half-volume spectrum of a manifold $M$. This is analogous to the usual volume spectrum, except that we restrict to p-sweepouts whose slices are each required to enclose half the volume of $M$. We use the Allen-Cahn min-max theory to find hypersurfaces associated to the half-volume spectrum. Each hypersurface consists of a constant mean curvature component enclosing half the volume of $M$ plus a (possibly empty) collection of minimal components.
2022-02-16T00:00:00+01:00
Liam Mazurowski
Researchers
en
https://www.carmin.tv/uploads/video/video-c10eb7dc682a817721f86e8627e64578.jpg
oai:carmin.tv:currents-on-metric-spaces-and-intrinsic-flat-convergence
2023-02-10T19:06:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:currents-on-metric-spaces-and-intrinsic-flat-convergence
https://www.carmin.tv/fr/video/currents-on-metric-spaces-and-intrinsic-flat-convergence
Currents on metric spaces and intrinsic flat convergence
video/mp4
IHES
First I will provide a brief introduction to Ambrosio-Kirchheim’s Theory of Currents on Metric Spaces. Then I will review joint work with Wenger defining integral current spaces and intrinsic flat convergence. This will provide sufficient background needed to follow the talk of Antoine Song.
2023-02-02T00:00:00+01:00
Christina Sormani
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-a9ae95ecc9804d9f5a88e84d314b103b.jpg
oai:carmin.tv:spherical-plateau-problem-and-applications
2023-02-10T19:04:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:spherical-plateau-problem-and-applications
https://www.carmin.tv/fr/video/spherical-plateau-problem-and-applications
Spherical Plateau problem and applications
video/mp4
IHES
I will discuss an area minimization problem in certain quotients of the Hilbert sphere by countable groups. An early version of that setting appears in Besson-Courtois-Gallot’s work on the entropy inequality. As an application of this minimization problem, we obtain some stability results. For instance, consider a closed surface of genus at least $2$ endowed with a Riemannian metric $g$, and let $(S,g)$ be its universal cover. After normalizing $g$ so that the volume entropy of $(S,g)$ is $1$, it is well-known that the first eigenvalue $\lambda$ is at most $\frac14$, and equality holds if $g$ is a hyperbolic metric. The hyperbolic plane is in fact stable: if $\lambda$ is close to the upper bound $\frac14$, then $(S,g)$ is close to the hyperbolic plane in a Benjamini-Schramm topology.
2022-12-09T00:00:00+01:00
Antoine Song
Researchers
en
https://www.carmin.tv/uploads/video/video-e931cf905bc708e26431af36e8708cd8.jpg
oai:carmin.tv:lipschitz-constant-and-degree-of-mappings
2022-12-30T18:04:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:lipschitz-constant-and-degree-of-mappings
https://www.carmin.tv/fr/video/lipschitz-constant-and-degree-of-mappings
Lipschitz constant and degree of mappings
video/mp4
IHES
We will survey the connection between the Lipschitz constant of a map $f$ (between Riemannian manifolds) and the topological type of the map. We will mostly focus on the degree of the map, because the story is already quite complex in that case. If $f\colon M^n \to M^n$ has Lipschitz constant $L$, then the degree of $f$ is at most $L^n$. When $M$ is $S^n$, there are self maps with Lipschitz constant $L$ and degree at least $c_n L^n$. But what happens for other manifolds? We will survey recent developments on this question by Aleksandr Berdnikov and Fedor Manin. We will see some clever maps that are somewhat related to the maps Robert will talk about in the following talk.
2022-12-09T00:00:00+01:00
Larry Guth
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-1922d9474e50de1b6cadd9e1839b0355.jpg
oai:carmin.tv:self-similar-solutions-to-extension-and-approximation-problems
2022-12-31T21:27:30+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:self-similar-solutions-to-extension-and-approximation-problems
https://www.carmin.tv/fr/video/self-similar-solutions-to-extension-and-approximation-problems
Self-similar solutions to extension and approximation problems
video/mp4
IHES
In 1979, Kaufman constructed a remarkable surjective Lipschitz map from a cube to a square whose derivative has rank 1 almost everywhere. In this talk, we will present some higher-dimensional generalizations of Kaufman's construction that lead to Lipschitz and Hölder maps with wild properties, including: topologically nontrivial maps from $S^m$ to $S^n$ with derivative of rank $n-1$, $\frac{2}{3}-\epsilon$--Hölder approximations of surfaces in the Heisenberg group, and Hölder maps from the disc to the disc that preserve signed area but approximate an arbitrary continuous map.
2022-12-09T00:00:00+01:00
Robert Young
Researchers
en
https://www.carmin.tv/uploads/video/video-c61ad903b82a5dc02dba1b318f777f30.jpg
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-4-4
2022-12-09T12:20:01+01:00
videos:institution:ihes
videos:collection:yilin-wang-the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-4-4
https://www.carmin.tv/fr/video/the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-4-4
The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory (4/4)
video/mp4
IHES
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle and connect it to determinants of Laplacians. Furthermore, the Loewner energy is a Kahler potential on the Weil-Petersson Teichmueller space identified with the space of Weil-Petersson quasicircles. Intriguingly, this class of finite energy curves has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and has been studied since the eighties with motivations from string theory. The myriad of perspectives on this class of curves is both luxurious and mysterious.
I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on. I will highlight how ideas from random conformal geometry inspire new results on Weil-Petersson quasicircles and discuss further directions.
2022-12-08T00:00:00+01:00
Yilin Wang
large deviation principle, Schramm-Loewner evolution, Loewner energy, Weil-Petersson Teichmueller space, determinants of Laplacian, random conformal geometry, Researchers, Graduate Students
en
Yilin Wang – The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory / 30/11/2022 - 08/12/2022
https://www.carmin.tv/uploads/video/video-ec7efa5c29e75b473d22e64a72560b7c.jpg
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-3-4
2022-12-07T20:54:01+01:00
videos:institution:ihes
videos:collection:yilin-wang-the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-3-4
https://www.carmin.tv/fr/video/the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-3-4
The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory (3/4)
video/mp4
IHES
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle and connect it to determinants of Laplacians. Furthermore, the Loewner energy is a Kahler potential on the Weil-Petersson Teichmueller space identified with the space of Weil-Petersson quasicircles. Intriguingly, this class of finite energy curves has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and has been studied since the eighties with motivations from string theory. The myriad of perspectives on this class of curves is both luxurious and mysterious.
I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on. I will highlight how ideas from random conformal geometry inspire new results on Weil-Petersson quasicircles and discuss further directions.
2022-12-07T00:00:00+01:00
Yilin Wang
large deviation principle, Schramm-Loewner evolution, Loewner energy, Weil-Petersson Teichmueller space, determinants of Laplacian, random conformal geometry, Researchers, Graduate Students
en
Yilin Wang – The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory / 30/11/2022 - 08/12/2022
https://www.carmin.tv/uploads/video/video-cacd22ab5dff270125fd9a732eb0e8cc.jpg
oai:carmin.tv:fonctions-spheroidales-et-triplets-spectraux-1
2022-12-06T23:40:02+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:fonctions-spheroidales-et-triplets-spectraux-1
https://www.carmin.tv/fr/video/fonctions-spheroidales-et-triplets-spectraux-1
Fonctions sphéroïdales et triplets spectraux
video/mp4
IHES
J'expliquerai la construction à partir de l'opérateur différentiel W du second ordre qui apparait par séparation des variables dans le Laplacien d'un ellipsoide, et des fonctions propres de W, de triplets spectraux reproduisant les comportement infrarouge et ultraviolets des zeros de zeta. Ce sont des résultats récents en collaboration avec Katia Consani et Henri Moscovici.
2022-12-02T00:00:00+01:00
Alain Connes
Researchers
fr
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-247f0ffefe5e484bd1ac6b0962fa838c.jpg
oai:carmin.tv:le-probleme-du-bicentralisateur-de-connes
2022-12-04T01:28:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:le-probleme-du-bicentralisateur-de-connes
https://www.carmin.tv/fr/video/le-probleme-du-bicentralisateur-de-connes
Le problème du bicentralisateur de Connes
video/mp4
IHES
À la fin des années 1970, Connes formula une conjecture portant sur les facteurs de type III1 connue sous le nom de "problème du bicentralisateur" et montra qu'une solution positive à ce problème permettrait de prouver l'unicité du facteur moyennable de type III1. Cette conjecture de Connes fut résolue dans le cas des facteurs moyennables par Haagerup en 1984. Mais elle reste encore largement ouverte aujourd'hui dans le cas non moyennable. Dans cet exposé, j'expliquerai le problème du bicentralisateur, son histoire, ses motivations et je présenterai quelques résultats nouveaux obtenus ces dernières années.
2022-12-02T00:00:00+01:00
Amine Marrakchi
Researchers
fr
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-34dc2dd826e6b796c8b12ff3882e6c56.jpg
oai:carmin.tv:the-godbillon-vey-invariant-in-theory-with-real-coefficients
2022-12-04T01:30:02+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:the-godbillon-vey-invariant-in-theory-with-real-coefficients
https://www.carmin.tv/fr/video/the-godbillon-vey-invariant-in-theory-with-real-coefficients
The Godbillon-Vey Invariant in 𝐾𝐾-theory with Real coefficients
video/mp4
IHES
2022-12-02T00:00:00+01:00
Sara Azzali
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-6db3e0f7100f6c49cbfb5a09c79c9ec5.jpg
oai:carmin.tv:quantum-automorphism-groups-of-some-classes-of-graphs
2022-12-04T01:32:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:quantum-automorphism-groups-of-some-classes-of-graphs
https://www.carmin.tv/fr/video/quantum-automorphism-groups-of-some-classes-of-graphs
Quantum Automorphism Groups of Some Classes of Graphs
video/mp4
IHES
Simple combinatorial objects like finite graphs can reveal hidden endemically quantum behaviors. In the same way that the symmetries of a graph are encoded in its automorphism group, its quantum symmetries are encoded in its quantum automorphism group. Surprisingly, the latter can be very different from the former, and a graph can have much more symmetries in the quantum world than it has in the classical world. In this talk, after introducing the topic, I will present some of these examples as well as recent computations of quantum automorphism groups for some classes of graphs.
2022-12-02T00:00:00+01:00
Paul Meunier
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-8e05ef4dbdecb72d430f2843cb6324f5.jpg
oai:carmin.tv:schatten-properties-of-commutators
2022-12-04T01:54:03+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:schatten-properties-of-commutators
https://www.carmin.tv/fr/video/schatten-properties-of-commutators
Schatten Properties of Commutators
video/mp4
IHES
Given a quantum tori $\mathbb{T}_{\theta}^d$, we can define the Riesz transforms $\mathfrak{R}_j$ on the quantum tori and the commutator $đx_i$ := [$\mathfrak{R}_i,M_x$], where $M_x$ is the operator on $L^2(\mathbb{T}_{\theta}^d)$ of pointwise multiplication by $x \in L^\infty (\mathbb{T}_{\theta}^d)$. In this talk, we will characterize the Schatten properties of the commutator [$\mathfrak{R}_i,M_x$] by showing that $x \in B_{p,q}^{\alpha} ({\mathbb T}_{\theta}^d)$, where $B_{p,q}^{\alpha} ({\mathbb T}_{\theta}^d)$ is the Besov space on quantum tori. Futhermore, we will extend this characterisation to the more general case where $\mathfrak{R}_j$ replaced by an arbitrary Calderon-Zygmund operator. To date, these new results treat the quantum differentiability in the strictly noncommutative setting.
2022-12-02T00:00:00+01:00
Kai Zeng
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-c0f4718da7e81e815d99be90e82a3bae.jpg
oai:carmin.tv:paires-de-hecke-et-k-theorie
2022-12-04T01:56:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:paires-de-hecke-et-k-theorie
https://www.carmin.tv/fr/video/paires-de-hecke-et-k-theorie
Paires de Hecke et K-théorie
video/mp4
IHES
Introduites par Shimura en théorie des nombres dans les années 50, les paires de Hecke sont des inclusions de sous-groupes qui sont presque normales : leurs conjugués sont tous commensurables. À une paire de Hecke est associée un groupe localement compact totalement discontinu : sa complétion de Schlichting.
Dans cet exposé, nous relions l’existence de sous-groupes presque normaux à la géométrie à grande échelle des complétions de Schlichting. Cela permet de prouver divers résultats de stabilité pour les conjectures de Baum-Connes et de Novikov, et de les valider sur de nouveaux exemples. Si le temps le permet, nous présenterons un travail en cours sur l’application de ces techniques au calcul de K-théorie de C*-algèbres de Hecke.
2022-12-02T00:00:00+01:00
Clément Dell’aiera
Researchers
fr
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-7b00f7211ecb18786ae412373a170b9e.jpg
oai:carmin.tv:schatten-properties-for-noncommutative-martingale-paraproduct
2022-12-04T01:58:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:schatten-properties-for-noncommutative-martingale-paraproduct
https://www.carmin.tv/fr/video/schatten-properties-for-noncommutative-martingale-paraproduct
Schatten Properties for Noncommutative Martingale Paraproduct
video/mp4
IHES
As is well-known, the martingale paraproducts are Hankel-type operators. In this talk, I will present some Schatten class memberships of the d-adic martingale paraproducts in the semi-commutative setting. Then I will use the transference method to give a characterization of the Sp-norms of the martingale paraproducts for some particular noncommutative martingales
2022-12-02T00:00:00+01:00
Zhenguo Wei
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-2e715cb432916e23e796ec9a641f994a.jpg
oai:carmin.tv:fonctions-spheroidales-et-triplets-spectraux
2022-12-04T12:46:02+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:fonctions-spheroidales-et-triplets-spectraux
https://www.carmin.tv/fr/video/fonctions-spheroidales-et-triplets-spectraux
Fonctions sphéroïdales et triplets spectraux
video/mp4
IHES
J'expliquerai la construction à partir de l'opérateur différentiel W du second ordre qui apparait par séparation des variables dans le Laplacien d'un ellipsoide, et des fonctions propres de W, de triplets spectraux reproduisant les comportement infrarouge et ultraviolets des zeros de zeta. Ce sont des résultats récents en collaboration avec Katia Consani et Henri Moscovici.
2022-12-02T00:00:00+01:00
Alain Connes
Researchers
fr
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-36dea5f5ee987cedd6a27514437ba681.jpg
oai:carmin.tv:proprietes-de-relevement-pour-les-algebres-du-local-au-global
2022-12-04T01:40:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:proprietes-de-relevement-pour-les-algebres-du-local-au-global
https://www.carmin.tv/fr/video/proprietes-de-relevement-pour-les-algebres-du-local-au-global
Propriétés de relèvement pour les 𝐶^∗-algèbres : du local au global ?
video/mp4
IHES
The main problem we will consider is whether the local lifting property (LLP) of a $C^*$-algebra implies the (global) lifting property (LP). Kirchberg showed that this holds if the Connes embedding problem has a positive solution, but it might hold even if its solution is negative. We will present several new characterizations of the lifting property for a $C^*$-algebra $A$ in terms of the maximal tensor product of A with the (full) $C^*$-algebra of the free group ${\mathbb F}_{\infty}$. We will recall our recent construction of a non-exact $C^*$-algebra with both LLP and WEP. This prompted us to try to prove that LLP implies LP for a WEP $C^*$-algebra. While our investigation is not conclusive we obtain a fairly simple condition in terms of tensor products that is equivalent to the validity of the latter implication.
2022-12-01T00:00:00+01:00
Gilles Pisier
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-ba62222bbe72f39cd2fe6d9f0566de67.jpg
oai:carmin.tv:non-commutative-pointwise-ergodic-theorem-for-actions-of-amenable-groups
2022-12-04T01:44:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:non-commutative-pointwise-ergodic-theorem-for-actions-of-amenable-groups
https://www.carmin.tv/fr/video/non-commutative-pointwise-ergodic-theorem-for-actions-of-amenable-groups
Non-commutative Pointwise Ergodic Theorem for Actions of Amenable Groups
video/mp4
IHES
Birkhoff's famous theorem asserts the pointwise convergence of ergodic averages associated with a measure preserving transformation of a measure space. In this talk, I will discuss generalizations of this theorem in two directions: the transformation will be replaced by the action of an amenable group, and the measure space by a von Neumann algebra equipped with a trace. A central role will be played by the notion of non-commutative maximal function, which extends for our purposes the notion of supremum to families of operators. The talk is based on joint work with Simeng Wang.
2022-12-01T00:00:00+01:00
Léonard Cadilhac
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-726db6a2676ea7b8cd57f0e4b19aa12c.jpg
oai:carmin.tv:tracial-and-g-invariant-states-on-quantum-groups
2022-12-04T01:46:02+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:tracial-and-g-invariant-states-on-quantum-groups
https://www.carmin.tv/fr/video/tracial-and-g-invariant-states-on-quantum-groups
Tracial and G-invariant States on Quantum Groups
video/mp4
IHES
For a discrete group G, the tracial states on its reduced group $C^*$-algebra $C^∗_r (G)$ are exactly the conjugation invariant states. This makes the traces on $C^∗_r (G)$ amenable to group dynamical techniques. In the setting of a discrete quantum group ${\mathbb G}$, there is a quantum analog of the conjugation action of $G$ on $C^∗_r (G)$. Recent work of Kalantar, Kasprzak, Skalski, and Vergnioux shows that ${\mathbb G}$-invariant states on the quantum group reduced $C^*$-algebra $C_r( \widehat{\mathbb G})$ are in one-to-one correspondence with certain KMS-states, exhibiting a disparity between tracial states and ${\mathbb G}$-invariant states unless ${\mathbb G}$ is unimodular. We will show there is still enough of a connection between traceability and G-invariance to say interesting things about the tracial states of $C_r( \widehat{\mathbb G})$.
2022-12-01T00:00:00+01:00
Benjamin Anderson-Sackaney
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-f1b23f24d9615e2ee923123a7cbf19c6.jpg
oai:carmin.tv:from-the-littlewood-paley-stein-inequality-to-the-burkholder-gundy-inequality
2022-12-04T01:48:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:from-the-littlewood-paley-stein-inequality-to-the-burkholder-gundy-inequality
https://www.carmin.tv/fr/video/from-the-littlewood-paley-stein-inequality-to-the-burkholder-gundy-inequality
From the Littlewood-Paley-Stein Inequality to the Burkholder-Gundy Inequality
video/mp4
IHES
We solve a question asked by Xu about the order of optimal constants in the Littlewood-Paley-Stein inequality. This relies on a construction of a special diffusion semi-group associated with a martingale which relates the Littlewood G-function with the martingale square function pointwise. This can also be done in vector-valued and noncommutative cases.
2022-12-01T00:00:00+01:00
Xu Zhendong
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-1534077f8a7e15ed4a27a0be65bacd07.jpg
oai:carmin.tv:schoenberg-correspondence-and-semigroup-of-k-super-positive-operators
2022-12-04T01:48:01+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:schoenberg-correspondence-and-semigroup-of-k-super-positive-operators
https://www.carmin.tv/fr/video/schoenberg-correspondence-and-semigroup-of-k-super-positive-operators
Schoenberg Correspondence and Semigroup of k-(super)positive Operators
video/mp4
IHES
The famous Lindblad, Kossakowski, Gorini, and Sudarshan's (LKGS) theorem characterizes the generator of a semigroup of completely positive maps. Motivated by this result we study the characterization of the generators of other positive maps e.g. k-positive and k-super positive maps. We prove a Schoenberg-type correspondence for a general non-unital semigroup of operators and apply this result to different cones of positive operators in $L(M_n, M_n)$ which are interesting for quantum information. As a corollary of our result, we re-establish the LKGS's theorem.
2022-12-01T00:00:00+01:00
Purbayan Chakraborty
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-6af224e07d98345da408803a39cab3fc.jpg
oai:carmin.tv:free-wreath-products-as-fundamental-graph-c-algebras
2022-12-04T01:52:02+01:00
videos:institution:ihes
videos:collection:arbre-de-noel-du-gdr-geometrie-non-commutative
oai:carmin.tv:free-wreath-products-as-fundamental-graph-c-algebras
https://www.carmin.tv/fr/video/free-wreath-products-as-fundamental-graph-c-algebras
Free Wreath Products as Fundamental Graph C*-algebras
video/mp4
IHES
The free wreath product of a compact quantum group by the quantum permutation group S+N has been introduced by Bichon in order to give a quantum counterpart of the classical wreath product. The representation theory of such groups is well-known, but some results about their operator algebras were still open, for example, the Haagerup property, K-amenability, or factoriality of the von Neumann algebra. I will present a joint work with Pierre Fima in which we identify these algebras with the fundamental 𝐶^∗-algebras of certain graphs of 𝐶^∗-algebras, and we deduce these properties from these constructions
2022-12-01T00:00:00+01:00
Arthur Troupel
Researchers
en
Arbre de Noël du GDR « Géométrie non-commutative » / La géométrie non-commutative, fondée par Alain Connes, est un domaine de recherche important des mathématiques actuelles. Le GDR "Géométrie Non-commutative" du CNRS regroupe l'ensemble des chercheurs français travaillant sur des thématiques en lien avec ce domaine. La parole y est donnée aux jeunes chercheurs du domaine, doctorants et post-doctorants, qui peuvent ainsi présenter leurs travaux à la communauté. Quelques exposés de chercheurs confirmés complètent cette rencontre en offrant un panorama des évolutions actuelles. / Amaury Freslon, Maria-Paula Gomez-Aparicio / 01/12/2022 - 02/12/2022 / https://indico.math.cnrs.fr/event/8849/
https://www.carmin.tv/uploads/video/video-e70f92fcae3fea1dea133f1debd5a1e1.jpg
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-2-4
2022-12-02T01:16:01+01:00
videos:institution:ihes
videos:collection:yilin-wang-the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-2-4
https://www.carmin.tv/fr/video/the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-2-4
The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory (2/4)
video/mp4
IHES
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle and connect it to determinants of Laplacians. Furthermore, the Loewner energy is a Kahler potential on the Weil-Petersson Teichmueller space identified with the space of Weil-Petersson quasicircles. Intriguingly, this class of finite energy curves has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and has been studied since the eighties with motivations from string theory. The myriad of perspectives on this class of curves is both luxurious and mysterious.
I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on. I will highlight how ideas from random conformal geometry inspire new results on Weil-Petersson quasicircles and discuss further directions.
2022-12-01T00:00:00+01:00
Yilin Wang
large deviation principle, Schramm-Loewner evolution, Loewner energy, Weil-Petersson Teichmueller space, determinants of Laplacian, random conformal geometry, Researchers, Graduate Students
en
Yilin Wang – The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory / 30/11/2022 - 08/12/2022
https://www.carmin.tv/uploads/video/video-778b3f724b9e138f0f43b6e98a42b25c.jpg
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-1-4
2022-11-30T20:52:01+01:00
videos:institution:ihes
videos:collection:yilin-wang-the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory
oai:carmin.tv:the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-1-4
https://www.carmin.tv/fr/video/the-loewner-energy-at-the-crossroad-of-random-conformal-geometry-and-teichmueller-theory-1-4
The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory (1/4)
video/mp4
IHES
The Loewner energy for Jordan curves first arises from the large deviations of Schramm-Loewner evolution (SLE), a family of random fractal curves modeling interfaces in 2D statistical mechanics. In a certain way, this energy measures the roundness of a Jordan curve, and we show that it is finite if and only if the curve is a Weil-Petersson quasicircle and connect it to determinants of Laplacians. Furthermore, the Loewner energy is a Kahler potential on the Weil-Petersson Teichmueller space identified with the space of Weil-Petersson quasicircles. Intriguingly, this class of finite energy curves has more than 20 equivalent definitions arising in very different contexts, including Teichmueller theory, geometric function theory, hyperbolic geometry, spectral theory, and has been studied since the eighties with motivations from string theory. The myriad of perspectives on this class of curves is both luxurious and mysterious.
I will overview the links between Loewner energy and SLE, Weil-Petersson quasicircles, and other branches of mathematics it touches on. I will highlight how ideas from random conformal geometry inspire new results on Weil-Petersson quasicircles and discuss further directions.
2022-11-30T00:00:00+01:00
Yilin Wang
large deviation principle, Schramm-Loewner evolution, Loewner energy, Weil-Petersson Teichmueller space, determinants of Laplacian, random conformal geometry, Researchers, Graduate Students
en
Yilin Wang – The Loewner Energy at the Crossroad of Random Conformal Geometry and Teichmueller Theory / 30/11/2022 - 08/12/2022
https://www.carmin.tv/uploads/video/video-c81cd0cd4958150760b1131c68942b97.jpg
oai:carmin.tv:combinatorics-of-the-amplituhedron
2022-11-30T13:06:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:combinatorics-of-the-amplituhedron
https://www.carmin.tv/fr/video/combinatorics-of-the-amplituhedron
Combinatorics of the amplituhedron
video/mp4
IHES
The amplituhedron is the image of the positive Grassmannian under a map in-
duced by a totally positive matrix. It was introduced by Arkani-Hamed and Trnka
to compute scattering amplitudes in N=4 super Yang Mills. I’ll give a gentle
introduction to the amplituhedron, surveying its connections to cluster algebras,
matroids, and combinatorics (Eulerian numbers, Narayana numbers, etc)
2022-11-29T00:00:00+01:00
Lauren Williams
Positive Grassmannian, cluster algebra, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-4615670901495a3ee7f4ad3b94a635d6.jpg
oai:carmin.tv:cluster-duality-and-non-holomorphic-spectral-curves
2022-11-30T13:08:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:cluster-duality-and-non-holomorphic-spectral-curves
https://www.carmin.tv/fr/video/cluster-duality-and-non-holomorphic-spectral-curves
Cluster duality and non-holomorphic spectral curves
video/mp4
IHES
Cluster duality is a correspondence between tropical points of a cluster A-variety
and a canonical basis of functions on the corresponding X-variety. (It is a gen-
eralization of duality between integers and the multiplicative group.) In the talk
we will suggest related geometric interpretations of the tropical points of the A-
variety for local system of the curve. On on hand it can be considered as a class
of graphs on the surfaces colored by generators of the affine Weyl group. This is
a generalization of the notion of a measured laminaiton. On the other hand it can
be interpreted as a class class of Lagrangian coverings in the cotangent bundle to
the curve representing integer classes of homology. Finally they are related to the
”cells” of the space of local system on the curve with values in the affine group.
(Joint with A.Thomas and V.Tatitscheff)
2022-11-29T00:00:00+01:00
Vladimir Fock
cluster varieties, character varieties, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-368bb969010ce323e9227db5780342e0.jpg
oai:carmin.tv:introduction-to-resurgence
2023-02-02T10:28:12+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:introduction-to-resurgence
https://www.carmin.tv/fr/video/introduction-to-resurgence
Introduction to resurgence
video/mp4
IHES
I will explain the phenomenon of resurgence in a (apparently) new ex-
ample related to Stirling formula, and its generalization to quantum dilogarithm.
Let us define rational Stirling numbers (St_k) = (1, 1/12, 1/288, . . . ) as coeffi-
cients in the asymptotic expansion of the normalized factorial:
$n ! \sim \sqrt{2\pi n} n^n e^{-n} (1 + \frac{1}{12n} + \frac{1}{288n²} - \frac{139}{51849n³} + \cdots)$ Then the asymptotic behavior of
St_k for large even k is controlled by numbers St_k for small odd k, and vice versa.
In the case of quantum dilogarithm one deforms Stirling numbers to Euler poly-
Nomials.
2022-11-29T00:00:00+01:00
Maxim Kontsevich
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-d4a8de218d9d968683a7eba584d26f2e.jpg
oai:carmin.tv:the-one-sided-cycle-shuffles-in-the-symmetric-group-algebra
2022-11-30T20:30:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:the-one-sided-cycle-shuffles-in-the-symmetric-group-algebra
https://www.carmin.tv/fr/video/the-one-sided-cycle-shuffles-in-the-symmetric-group-algebra
The one-sided cycle shuffles in the symmetric group algebra
video/mp4
IHES
We study a new family of elements in the group ring of a symmetric
group – or, equivalently, a class of ways to shuffle a deck of cards.
Fix a positive integer n. Consider the symmetric group S_n. For each 1 ≤ ℓ ≤
n, we define an element
t_ℓ := cyc_ℓ + cyc{ℓ,ℓ+1} + cyc_{ℓ,ℓ+1,ℓ+2} + · · · + cyc_{ℓ,ℓ+1,...,n}
of the group ring ${\mathbb R} [S_n]$, where cyc_{i₁,i₂,...,i_k} denotes the cycle that rotates through
the given elements i₁, i₂ , . . . , i_k . We refer to these n elements t₁, t₂, . . . , t_n as
the somewhere-to-below shuffles, since the standard interpretation of elements of
${\mathbb R} [S_n]$ in terms of card shuffling allows us to view them as shuffling operators.
Note that t₁ is the well-known top-to-random shuffle studied by Diaconis, Fill,
Pitman and others, whereas t_n = id.
Similar families of elements of ${\mathbb R} [S_n]$ include the Young-Jucys-Murphy el-
ements, the Reiner-Saliola-Welker elements, and the Diaconis-Fill-Pitman ele-
ments. Unlike the latter three families, the somewhere-to-below shuffles t₁, t₂, . . . , t_n
do not commute. However, they come close to commuting: There is a basis of
${\mathbb R} [S_n]$ on which they all act as upper-triangular matrices; thus, they generate an
algebra whose semisimple quotient is commutative (which entails, in particular,
that their commutators are nilpotent).
This basis can in fact be constructed combinatorially, and bears several un-
expected connections, most strikingly to the Fibonacci sequence. One of the
consequences is that any ${\mathbb R}$-linear combination λ₁ t₁ + λ₂ t₂ + · · · + λ_n t_n (with
λ₁ , λ₂ , . . . , λ_n ∈ {\mathbb R}) can be triangularized and its eigenvalues explicitly computed
(along with their multiplicities); the number of distinct eigenvalues is at most the
Fibonacci number f_{n+1}. If all these f_{n+1} eigenvalues are indeed distinct, then the
matrix is diagonalizable.
While we have been working over ${\mathbb R}$ for illustrative purposes, all our proofs
hold over any commutative ring (or, for the diagonalizability claim, over any
field). Several open questions remain (joint work with Nadia Lafrenière)
2022-11-29T00:00:00+01:00
Darij Grinberg
probability, representation theory, Markov chains, Symmetric group, symmetric group algebra, shuffles, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-0e468a4070ad0d3d144720c398497737.jpg
oai:carmin.tv:canonical-grothendieck-polynomials-with-free-fermions
2022-11-30T20:32:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:canonical-grothendieck-polynomials-with-free-fermions
https://www.carmin.tv/fr/video/canonical-grothendieck-polynomials-with-free-fermions
Canonical Grothendieck polynomials with free fermions
video/mp4
IHES
A now classical method to construct the Schur functions is constructing matrix el-
ements using half vertex operators associated to the classical boson-fermion cor-
respondence. This construction is known as using free fermions. Schur functions
are also known to be polynomial representatives of cohomology classes of Schu-
bert varieties in the Grassmannian. By instead using K-theory, the representatives
become the (symmetric) Grothendieck polynomials. A recent generalization was
given by Hwang et al. called the (refined) canonical Grothendieck polynomials
based on the work of Galashin–Grinberg–Liu and Yeliussizov. In this talk, we
take the Jacobi–Trudi formulas of Hwang et al. as our definition and use Wick’s
theorem to give a presentation for the canonical Grothendieck polynomials and
their dual basis using free fermions. This generalizing the recent work of Iwao.
Using this, we derive many known identities, as well as some new ones, through
simple computations. This is based on joint work with Shinsuke Iwao and Kohei
Motegi (arXiv: 2211.05002).
2022-11-29T00:00:00+01:00
Tim Scrimshaw
Grothendieck polynomial, free-fermion, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-19b05da46e51e76a53ccd63a07d5c8ed.jpg
oai:carmin.tv:statistical-models-on-random-regular-graphs
2022-11-30T20:34:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:statistical-models-on-random-regular-graphs
https://www.carmin.tv/fr/video/statistical-models-on-random-regular-graphs
Statistical models on random regular graphs
video/mp4
IHES
Using the matrix-forest theorem and the Parisi-Sourlas trick we formu-
late and solve a one-matrix model with non-polynomial potential which provides
perturbation theory for massive spinless fermions on dynamical planar graphs.
This is a version of 2d quantum gravity discretized via RRG coupled to massive
spinless fermions. Our model equivalently describes the ensemble of spanning
forests on the same graph. The solution is formulated in terms of an elliptic curve.
We then focus on a near-critical scaling limit when both the graphs and the trees in
the forests are macroscopically large. In this limit we obtain universal one-point
scaling functions (condensates), parameterized in terms of the Lambert function.
Our results provide a rare example where one can explore the flow between two
gravity models – in this case, the theories of conformal matter coupled to 2d grav-
ity with c=-2 (large trees regime) and c=0 (small trees regime). We shall also
present the results of numerical simulations concerning phase transitions in RRG
ensemble and their relation with Anderson localization.
2022-11-29T00:00:00+01:00
Alexander Gorsky
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-fe956d352401502824aa372da8c43532.jpg
oai:carmin.tv:reddening-sequences-for-cluster-algebras
2022-11-30T20:36:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:reddening-sequences-for-cluster-algebras
https://www.carmin.tv/fr/video/reddening-sequences-for-cluster-algebras
Reddening sequences for Cluster Algebras
video/mp4
IHES
While cluster algebras generally are not finitely generated, reddening
sequences offer a more relaxed notion of finiteness. The existence of a redden-
ing sequence has far reaching consequences for a cluster algebra (generic finite
dimensionality of the Jacobian, numeric Donaldson-Thomas invariants, canonical
bases). While it is not clear how to determine if a cluster algebra admits a redden-
ing sequence, in this talk we discuss some cases in which reddening sequences
have been established.
2022-11-29T00:00:00+01:00
Volker Genz
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-fee95b31f5feed06d494073d2d900cbf.jpg
oai:carmin.tv:on-the-positivity-of-meijer-g-functions
2022-11-30T20:38:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:on-the-positivity-of-meijer-g-functions
https://www.carmin.tv/fr/video/on-the-positivity-of-meijer-g-functions
On the positivity of Meijer G-functions
video/mp4
IHES
I will discuss some results and conjectures on the positivity of Meijer G-functions
on the positive half-line, in the non-trivial case where the underlying random vari-
able is not an independent product of quotients of beta random variables. Some
emphasis will be put on the notions of logarithmic infinite divisibility and quasi
infinite divisibility. If time permits, I will discuss some extensions to Fox H-
Functions.
2022-11-29T00:00:00+01:00
Thomas Simon
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-2b67935ca4f696b6ee9496d6791115f1.jpg
oai:carmin.tv:landau-ginzburg-potentials-via-projective-representations
2022-11-30T20:40:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:landau-ginzburg-potentials-via-projective-representations
https://www.carmin.tv/fr/video/landau-ginzburg-potentials-via-projective-representations
Landau-Ginzburg potentials via projective representations
video/mp4
IHES
Many interesting spaces arise as partial compactifications of Fock-Goncharov's cluster varieties, among them (affine cones over) flag varieties which are important objects in representation theory of algebraic groups. Due to a construction of Gross-Hacking-Keel-Kontsevich those partial compactifications give rise to Landau-Ginzburg potentials on the dual cluster varieties whose tropicalizations define interesting polyhedral cones parametrizing the theta basis on the ring of regular functions on the cluster varieties.
In this talk, after explaining the background, we give an interpretation of these Landau-Ginzburg potentials as F-polynomials of projective representations of Jacobian algebras. This is joint work with Daniel Labardini-Fragoso.
2022-11-29T00:00:00+01:00
Béa de Laporte
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-95aeb16666a6cbabc9c14270553910dc.jpg
oai:carmin.tv:kontsevichs-star-product-up-to-order-seven-for-affine-poisson-brackets-or-where-are-the-riemann-zeta
2022-11-30T20:54:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:kontsevichs-star-product-up-to-order-seven-for-affine-poisson-brackets-or-where-are-the-riemann-zeta
https://www.carmin.tv/fr/video/kontsevichs-star-product-up-to-order-seven-for-affine-poisson-brackets-or-where-are-the-riemann-zeta
Kontsevich’s star-product up to order seven for affine Poisson brackets, or:Where are the Riemann zeta values?
video/mp4
IHES
Noncommutative associative star-products are deformations of the usual product
of functions on smooth manifolds; in every star-product, its leading deformation
term is a Poisson bracket. Kontsevich’s star-products on finite-dimensional affine
Poisson manifolds are encoded using weighted graphs with ordering of directed
edges. The associativity is then obstructed only by the Jacobiator (and its differen-
tial consequences) for the bi-vector which starts the deformation. Finding the real
coefficients of graphs in Kontsevich’s star-product expansion is hard in practice;
conjecturally irrational Riemann zeta values appear from the firth order onwards.
In a joint work with R.Buring (arXiv:2209.14438 [q-alg]) we obtain the sev-
enth order formula of Kontsevich’s star-product for affine Poisson brackets (in
particular, for linear brackets on the duals of Lie algebras). We discover that all
the graphs near the Riemann ”zetas of concern” assimilate into differential conse-
quences of the Jacobi identity, so that all the coefficient in the star-product formula
are rational for every affine Poisson bracket. Thirdly, we explore the mechanism
of associativity for Kontsevich’s star-product for generic or affine Poisson brackets
(and with harmonic propagators from the original formula for the graph weights
): here, we contrast the work of this mechanism up to order six with the way
associativity works in terms of graphs for orders seven and higher.
2022-11-29T00:00:00+01:00
Arthemy Kiselev
deformation quantization, Kontsevich’s star-product, diagrammatic algebra, affine Poisson bracket, Riemann zeta, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-c9eb84a2ff138488a09437e585df1ba3.jpg
oai:carmin.tv:a-gentle-introduction-to-template-games-and-linear-logic
2022-11-30T02:04:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:a-gentle-introduction-to-template-games-and-linear-logic
https://www.carmin.tv/fr/video/a-gentle-introduction-to-template-games-and-linear-logic
A gentle introduction to template games and linear logic
video/mp4
IHES
Game semantics is the art of interpreting formulas (or types) as games and proofs
(or programs) as strategies. In order to reflect the interactive behaviour of pro-
grams, strategies are required to follow specific scheduling policies. Typically, in
the case of a sequential programming language, the program (Player) and its envi-
ronment (Opponent) play one after the other, in a strictly alternating way. On the
other hand, in the case of a concurrent language, Player and Opponent are allowed
to play several moves in a row, in a non alternating way. In the two cases, the
scheduling policy is designed very carefully in order to ensure that the strategies
synchronise properly and compose well when plugged together. A longstanding
conceptual problem has been to understand when and why a given scheduling
policy works and is compositional in that sense. In this talk, I will introduce the
notion of template game and exhibit a number of simple and fundamental combi-
natorial properties which ensure that a given scheduling policy defines (indeed) a
monoidal closed bicategory of games, strategies and simulations. The notion of
template game will be illustrated by constructing two game models of linear logic
with different flavours (alternating and asynchronous) using the same categorical
combinatorics, performed in the category of small 2-categories.
2022-11-28T00:00:00+01:00
Paul-André Melliès
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-09387cf1e181d4e9666f56f1b10531a1.jpg
oai:carmin.tv:substitutions-in-non-commutative-multivariate-power-series
2022-11-30T02:06:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:substitutions-in-non-commutative-multivariate-power-series
https://www.carmin.tv/fr/video/substitutions-in-non-commutative-multivariate-power-series
Substitutions in non-commutative multivariate power series
video/mp4
IHES
We describe a group law on formal power series in non-commuting variables in-
duced by their interpretation as linear forms on a Hopf algebra of sentences. We
study the corresponding structures and show how they can be used to recast in a
group theoretic form various identities and transformations on formal power se-
ries that have been central in the context of non-commutative probability theory.
Based on a joint work with K. Ebrahimi-Fard, N. Tapia and L. Zambotti.
2022-11-28T00:00:00+01:00
Frédéric Patras
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-88b0c11e5f0f79ba0968c874bc5597f7.jpg
oai:carmin.tv:a-gentle-introduction-to-template-games-and-linear-logic-1
2022-11-30T12:46:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:a-gentle-introduction-to-template-games-and-linear-logic-1
https://www.carmin.tv/fr/video/a-gentle-introduction-to-template-games-and-linear-logic-1
A gentle introduction to template games and linear logic
video/mp4
IHES
Game semantics is the art of interpreting formulas (or types) as games and proofs
(or programs) as strategies. In order to reflect the interactive behaviour of pro-
grams, strategies are required to follow specific scheduling policies. Typically, in
the case of a sequential programming language, the program (Player) and its envi-
ronment (Opponent) play one after the other, in a strictly alternating way. On the
other hand, in the case of a concurrent language, Player and Opponent are allowed
to play several moves in a row, in a non alternating way. In the two cases, the
scheduling policy is designed very carefully in order to ensure that the strategies
synchronise properly and compose well when plugged together. A longstanding
conceptual problem has been to understand when and why a given scheduling
policy works and is compositional in that sense. In this talk, I will introduce the
notion of template game and exhibit a number of simple and fundamental combi-
natorial properties which ensure that a given scheduling policy defines (indeed) a
monoidal closed bicategory of games, strategies and simulations. The notion of
template game will be illustrated by constructing two game models of linear logic
with different flavours (alternating and asynchronous) using the same categorical
combinatorics, performed in the category of small 2-categories.
2022-11-28T00:00:00+01:00
Paul-André Melliès
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-839b7c8e0809890d161734f23ea3d081.jpg
oai:carmin.tv:strange-gradings-and-elimination-of-generators
2022-11-30T01:48:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:strange-gradings-and-elimination-of-generators
https://www.carmin.tv/fr/video/strange-gradings-and-elimination-of-generators
Strange gradings and elimination of generators
video/mp4
IHES
Elimination of generators (commutative or noncommutative) is linked
to many combinatorial theories (Bisection and codes, Semidirect products of pre-
sented groups and Lie algebras, Strange gradings over semigroups, Lazard elim-
ination). We will describe unifying (categorical) links between some of these
theories and give general results allowing to get semidirect decompositions at first
sight.
(Joint work with Paul-André Melliès and Vu Nguyen Dinh.)
2022-11-28T00:00:00+01:00
Gérard Duchamp
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-6d1b7effe86239a9c41b3e4a97a593f3.jpg
oai:carmin.tv:random-lattices-as-sphere-packings
2022-11-30T01:50:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:random-lattices-as-sphere-packings
https://www.carmin.tv/fr/video/random-lattices-as-sphere-packings
Random lattices as sphere packings
video/mp4
IHES
In 1945, Siegel showed that the expected value of the lattice-sums of a function
over all the lattices of unit covolume in an n-dimensional real vector space is
equal to the integral of the function. In 2012, Venkatesh restricted the lattice-
sum function to a collection of lattices that had a cyclic group of symmetries and
proved a similar mean value theorem. Using this approach, new lower bounds
on the most optimal sphere packing density in n dimensions were established for
infinitely many n.
In the talk, we will outline some analogues of Siegel’s mean value theorem
over lattices. This approach has modestly improved some of the best known lattice
packing bounds in many dimensions. We will also show how such results can be
made effective and talk of some variations.
(Joint work with Vlad Serban.)
2022-11-28T00:00:00+01:00
Nihar Gargava
lattices, Sphere packing problem, Codes, Division rings, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-29545c7dc7859d4a10b08b6d7aca2208.jpg
oai:carmin.tv:geometry-and-physics-of-covalent-network-glasses
2022-11-30T01:52:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:geometry-and-physics-of-covalent-network-glasses
https://www.carmin.tv/fr/video/geometry-and-physics-of-covalent-network-glasses
Geometry and physics of covalent network glasses
video/mp4
IHES
Glasses are characterized by the absence of long-range order which
defines crystalline materials. However, they possess a rich and varied array of
short to medium range order, which originates from chemical bonding and related
interactions. whereas covalent systems (mostly chalcogenides like As-Se, Ge-As-
Se systems) or oxides (borate, boro-silicate and silicate glasses), have sparsely
packed, strongly bound network structures, like tetrahedral SiO2 units or B3O3
boroxol rings. These very different structures results in different physical proper-
ties and applications.
We present a simple mathematical model of glass transition based on the anal-
ysis of molecular agglomeration in overcooled liquids. The model uses the space
of probabilities of appearance of given local structures, and their slow time evo-
lution during annealing from a liquid melt. The evolution of probabilities is de-
scribed as action of an appropriate stochactis matrix. The glass transition is de-
fined as a fixed point resulting from the requirement of maximal homogeneity.
With simple assumptions concerning local configurations and their bonding en-
ergies, and with elementary combinatorics we are able to derive the dependence
of the glass transition temperature Tg on chemical composition in non-organic
covalent glasses. Numerous examples are shown to confirm the validity of the
stochastic agglomeration model.
2022-11-28T00:00:00+01:00
Richard Kerner
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-aef3dee09ce09a016792b8f6364b7cfe.jpg
oai:carmin.tv:phase-transitions-of-composition-schemes-and-their-universal-limit-laws
2022-11-30T02:00:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:phase-transitions-of-composition-schemes-and-their-universal-limit-laws
https://www.carmin.tv/fr/video/phase-transitions-of-composition-schemes-and-their-universal-limit-laws
Phase transitions of composition schemes and their universal limit laws
video/mp4
IHES
Multitudinous combinatorial structures are counted by generating functions satisfying a composition scheme $F(z)=G(H(z))$.
The corresponding asymptotic analysis becomes challenging when this scheme is critical
(i.e., $G$ and~$H$ are simultaneously singular).
The singular exponents appearing in the Puiseux expansions of $G$ and $H$ then dictate the asymptotics.
Motivated by many examples (random mappings, planar maps, directed lattice paths),
we consider a natural extension of this scheme, namely $F(z,u)=G(u H(z))M(z)$.
We also consider a variant of this scheme, which allows us to analyse the number of $H$-components of a given size in~$F$.
These two models lead to a rich world of limit laws, involving Mittag-Leffler distributions, stable distributions...
We prove (double) phase transitions, additionally involving Boltzmann and mixed Poisson distributions, with a unified explanation of the associated thresholds.
We explain why and when phase transitions involving a window of size $n^{1/3}$ are universal.
Applications are presented for random walks, trees (supertrees of trees, increasingly labelled trees, preferential attachment trees),
and for some extension of works of Flajolet (on the Airy distribution for planar maps), of Pitman (on the Chinese restaurant process), of Janson (on triangular P\'olya urns) ...
Joint work with Markus Kuba and Michael Wallner.
2022-11-28T00:00:00+01:00
Cyril Banderier
phase transitions, analytic combinatorics, Mittag-Leffler distributions, stable laws, Boltzmann distributions, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-7b049f5002d6d4479c5da8174c814e81.jpg
oai:carmin.tv:creative-telescoping-for-the-canham-model-in-genus-1
2022-11-30T01:54:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:creative-telescoping-for-the-canham-model-in-genus-1
https://www.carmin.tv/fr/video/creative-telescoping-for-the-canham-model-in-genus-1
Creative Telescoping for the Canham model in genus 1
video/mp4
IHES
The algorithmic method of Creative Telescoping turns out to be an extremely use-
ful tool in experimental mathematics, when dealing with concrete mathematical
problems. As striking examples, it can be used to compute and prove automati-
cally: a recurrence satisfied by any binomial sum (like the Ap ́ery numbers), the
equality of two period functions (in the sense of Kontsevich and Zagier), or a re-
currence for the moments of a measure.
In this talk, I will explain some theory behind Creative Telescoping, and show how
it can be applied in practice on a problem originating from biological physics. The
problem concerns the shape of biomembranes, such as blood cells, and examines
the uniqueness of the variational Helfrich problem in the case of genus 1 with a
prescribed isoperimetric ratio. This question boils down to computing the surface
area and volume of a projection of the Clifford torus in terms of Gaussian hyper-
geometric functions. We tackle this using Creative Telescoping, and then prove
that the rescaled ratio of these functions is monotonically increasing. The talk will
be based on joint work with Alin Bostan and Thomas Yu
2022-11-28T00:00:00+01:00
Sergey Yurkevich
Symbolic Integration, creative telescoping, period functions, Clifford torus, isoperimetric ratio, hypergeometric functions, Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-8ed88ae6ee16d5a014c78d0dc5d61fae.jpg
oai:carmin.tv:hausdorff-moment-problems-for-combinatorial-numbers-heuristics-via-meijer-g-functions
2022-11-30T01:56:01+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:hausdorff-moment-problems-for-combinatorial-numbers-heuristics-via-meijer-g-functions
https://www.carmin.tv/fr/video/hausdorff-moment-problems-for-combinatorial-numbers-heuristics-via-meijer-g-functions
Hausdorff moment problems for combinatorial numbers: heuristics via Meijer G-functions
video/mp4
IHES
We report on further investigations of combinatorial sequences in form of integral
ratios of factorials. We conceive these integers as Hausdorff power moments for
weights W (x), concentrated on the support x ∈ (0, R), and we solve this mo-
ment problem by furnishing the exact expressions for W (x)’s. In many instances
we can formally prove that the sequences are positive definite. We considered
a large set of families of such sequences including: formulas of Tutte et al. for
enumerations of planar maps, several generalizations of Catalan numbers such
as Fuss-Catalan and Raney numbers, the constellation numbers, and the ratios
of multiple factorials, such as the iconic Kontsevich ($\frac{(6n)!n !}{(3n)![(2n)!]²}$
And Chebyshev ($\frac{(30n)!n !}{(6n)!(10n)!(15n) !}$ ) sequences. Furthermore, we provide the exact solutions for all
three parametrized families of Bober ratios (2009) of factorials, as well as for the
”sporadic” ratios, for all of which the ordinary generating functions (ogf) are alge-
braic. Finally, in the same spirit, we studied the sequences recently constructed by
Rodriquez Villegas (2019-2022), including $\frac{(63n)!(8n)!(2n)!}{
n!(4n)!(16n)!(21n)!(31n)!}$ . In all the cases
listed above we have identified a precisely defined and persistent pattern relating
the Meijer G-encodings of appropriate ogf G(z) and of W (x). In fact, it appears
that in the language of Meijer G-functions, the solutions W (x) are practically
automatically obtained by reshuffling of data characterizing the ogf G(z) only,
i.e. the parameter lists and its radius of convergence R^{−1}. We attempt to cate-
gorize these observations and try to find the criteria for moments which would
allow for such an automatisation. It is also intriguing that the counterexamples
can be found, which clearly point to the limits of this procedure. Finding the pre-
cise criteria for moments which would permit for such a speedy method, is still a
challenging open problem.
⋆ Collaboration at various stages of this work with:
N. Behr, G. H. E. Duchamp, K. Górska, M. Kontsevich, and G. Koshevoy.
2022-11-28T00:00:00+01:00
Karol Penson
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-6de882be578281600d492ced607cee9e.jpg
oai:carmin.tv:categorification-of-rule-algebras
2022-11-30T02:02:02+01:00
videos:institution:ihes
videos:collection:combinatorics-and-arithmetic-for-physics-special-days-1
oai:carmin.tv:categorification-of-rule-algebras
https://www.carmin.tv/fr/video/categorification-of-rule-algebras
Categorification of Rule Algebras
video/mp4
IHES
Reporting on joint work in progress with P.-A. Melliès and N. Zeilberger, I will
present a novel approach to formalize operations in compositional rewriting sys-
tems wherein the number of ways to apply a rewrite is of interest. The approach
is based upon defining a suitable double category to capture individual rewriting
steps as its 2-cells, requiring in addition certain fibrational properties to hold for
the functors of vertical source and target as well as of horizontal composition of
cells. Counting numbers of realizations of individual rewriting steps or sequences
rewrites is then implemented via a presheaf calculus over 2-cells. I will demon-
strate how the notion of rule algebra representations is captured in this calculus
and how the rule algebras themselves are categorified via a categorical construc-
tion involving coends.
2022-11-28T00:00:00+01:00
Nicolas Behr
Researchers
en
Combinatorics and Arithmetic for Physics : Special Days / The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only.
Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. / Gérard H. E. Duchamp, Maxim Kontsevich, Gleb Koshevoy, Sergei Nechaev, and Karol A. Penson / 28/11/2022 - 29/11/2022 / https://indico.math.cnrs.fr/event/8730/
https://www.carmin.tv/uploads/video/video-9b9169e00b5087fd96283dd83c8ab046.jpg
oai:carmin.tv:theorie-des-cordes-et-theorie-des-nombres-valeurs-multiples-zeta-univaluees-elliptiques-et-formes-mo
2022-11-22T14:52:03+01:00
videos:institution:ihes
videos:collection:10eme-seminaire-itzykson-valeurs-zeta-multiples-et-fonctions-modulaires-de-graphes-en-theorie-des-co
oai:carmin.tv:theorie-des-cordes-et-theorie-des-nombres-valeurs-multiples-zeta-univaluees-elliptiques-et-formes-mo
https://www.carmin.tv/fr/video/theorie-des-cordes-et-theorie-des-nombres-valeurs-multiples-zeta-univaluees-elliptiques-et-formes-mo
Théorie des cordes et théorie des nombres : valeurs multiples zêta univaluées, elliptiques et formes modulaires
video/mp4
IHES
Dans ce cours nous présenterons les relations entre la théorie des nombres et les propriétés physiques des amplitudes. Nous présenterons la relation entre la condition d'univaluation des grandeurs physiques, et la notion introduite par Francis Brown. Nous discuterons le rôle de l'invariance modulaire et l'émergence de nouvelle formes modulaires.
2022-11-17T00:00:00+01:00
Pierre Vanhove
théorie des cordes, théorie des nombres, formes modulaires, fonction zêta, intégrales de Feynman, Researchers
fr
10ème Séminaire Itzykson : Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes / Dans leur développement à basse énergie, les amplitudes de diffusion en théorie des champs et en théorie des cordes ont des propriétés remarquables liées à la théorie des nombres, notamment en ce qui concerne l'invariance modulaire. Ainsi, certaines amplitudes sont déterminées par une classe de valeurs zêta multiples univaluées découvertes par Francis Brown. L'analyse des amplitudes de diffusion a conduit à la découverte de formes modulaires nouvelles généralisant au cas elliptique ces valeurs zêta multiples univaluées.
Durant cette journée seront présentés divers aspects de la relation entre les propriétés physiques des amplitudes, des développements récents en théorie des nombres, et de nouvelles formes modulaires.
Le cours présentera les notions fondamentales qui seront ensuite développées dans deux séminaires. / Maxim Kontsevich, Stéphane Nonnenmacher,Sylvain Ribault, Pierre Vanhove / 17/11/2022 - 17/11/2022 / https://indico.math.cnrs.fr/event/8429/
https://www.carmin.tv/uploads/video/video-bab0d3522b9305dd9651df7a4728e033.jpg
oai:carmin.tv:amplitudes-de-cordes-et-equations-de-type-knizhnik-zamolodchikov
2022-11-22T14:56:02+01:00
videos:institution:ihes
videos:collection:10eme-seminaire-itzykson-valeurs-zeta-multiples-et-fonctions-modulaires-de-graphes-en-theorie-des-co
oai:carmin.tv:amplitudes-de-cordes-et-equations-de-type-knizhnik-zamolodchikov
https://www.carmin.tv/fr/video/amplitudes-de-cordes-et-equations-de-type-knizhnik-zamolodchikov
Amplitudes de cordes et équations de type Knizhnik–Zamolodchikov
video/mp4
IHES
Les amplitudes de diffusion nous donnent la probabilité d'interaction des particules élémentaires. L'approche perturbative nous amène à considérer une série dont les coefficients sont calculés par les intégrales de Feynman. En théorie des cordes, un tel développement perturbatif est indexé par un entier qu'on peut interpréter comme le genre d'une surface. Dans la dernière décennie, l'effort conjoint de physiciens et mathématiciens a énormément amélioré notre compréhension des relations entre amplitudes des cordes ouvertes (reliées aux théories de jauge) et des cordes fermées (reliées à la gravité).
Je vais donner un aperçu de ces progrès, et notamment du rôle de l'équation de Knizhnik-Zamolodchikov et de ses généralisations en genre supérieur, et de la relation avec la théorie des périodes univaluées.
2022-11-17T00:00:00+01:00
Federico Zerbini
théorie des cordes, théorie des nombres, formes modulaires, fonction zêta, intégrales de Feynman, Researchers
fr
10ème Séminaire Itzykson : Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes / Dans leur développement à basse énergie, les amplitudes de diffusion en théorie des champs et en théorie des cordes ont des propriétés remarquables liées à la théorie des nombres, notamment en ce qui concerne l'invariance modulaire. Ainsi, certaines amplitudes sont déterminées par une classe de valeurs zêta multiples univaluées découvertes par Francis Brown. L'analyse des amplitudes de diffusion a conduit à la découverte de formes modulaires nouvelles généralisant au cas elliptique ces valeurs zêta multiples univaluées.
Durant cette journée seront présentés divers aspects de la relation entre les propriétés physiques des amplitudes, des développements récents en théorie des nombres, et de nouvelles formes modulaires.
Le cours présentera les notions fondamentales qui seront ensuite développées dans deux séminaires. / Maxim Kontsevich, Stéphane Nonnenmacher,Sylvain Ribault, Pierre Vanhove / 17/11/2022 - 17/11/2022 / https://indico.math.cnrs.fr/event/8429/
https://www.carmin.tv/uploads/video/video-f7fc2439ef403abe99c0c095e7e3674b.jpg
oai:carmin.tv:harnessing-sl-2-z-in-super-yang-mills-and-gravity
2022-11-22T15:00:01+01:00
videos:institution:ihes
videos:collection:10eme-seminaire-itzykson-valeurs-zeta-multiples-et-fonctions-modulaires-de-graphes-en-theorie-des-co
oai:carmin.tv:harnessing-sl-2-z-in-super-yang-mills-and-gravity
https://www.carmin.tv/fr/video/harnessing-sl-2-z-in-super-yang-mills-and-gravity
Harnessing SL(2, Z) in Super Yang–Mills and Gravity
video/mp4
IHES
We introduce a new approach to extracting the physical consequences of S-duality for observables of four-dimensional N=4 super Yang-Mills (SYM) theory. The main mathematical tool is the theory of harmonic analysis on the fundamental domain of SL(2,Z). Applying this technology leads to strong constraints on the analytic structure of observables in N=4 SYM. We treat a specific set of integrated correlators in some detail, which simplify drastically when expressed in the SL(2,Z)-invariant eigenbasis. We initiate the study of the statistics of CFT data in the ensemble of N=4 SYM theories. At large N, this has ramifications for holography. In a sense to be made precise, we show an equivalence between observables in the strongly coupled planar theory, dual to type IIB supergravity on AdS5 x S5, and their ensemble average over the N=4 SYM conformal manifold.
2022-11-17T00:00:00+01:00
Eric Perlmutter
modular forms, String theory, AdS/CFT correspondence, supersymmetric gauge theories, Researchers
en
10ème Séminaire Itzykson : Valeurs zêta multiples et fonctions modulaires de graphes en théorie des cordes / Dans leur développement à basse énergie, les amplitudes de diffusion en théorie des champs et en théorie des cordes ont des propriétés remarquables liées à la théorie des nombres, notamment en ce qui concerne l'invariance modulaire. Ainsi, certaines amplitudes sont déterminées par une classe de valeurs zêta multiples univaluées découvertes par Francis Brown. L'analyse des amplitudes de diffusion a conduit à la découverte de formes modulaires nouvelles généralisant au cas elliptique ces valeurs zêta multiples univaluées.
Durant cette journée seront présentés divers aspects de la relation entre les propriétés physiques des amplitudes, des développements récents en théorie des nombres, et de nouvelles formes modulaires.
Le cours présentera les notions fondamentales qui seront ensuite développées dans deux séminaires. / Maxim Kontsevich, Stéphane Nonnenmacher,Sylvain Ribault, Pierre Vanhove / 17/11/2022 - 17/11/2022 / https://indico.math.cnrs.fr/event/8429/
https://www.carmin.tv/uploads/video/video-4f14b05260767b8da348e169e3856c48.jpg
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-4-4
2022-11-22T16:29:23+01:00
videos:institution:ihes
videos:collection:slava-rychkov-random-field-ising-model-and-parisi-sourlas-supersymmetry
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-4-4
https://www.carmin.tv/fr/video/random-field-ising-model-and-parisi-sourlas-supersymmetry-4-4
Random Field Ising Model and Parisi-Sourlas Supersymmetry (4/4)
video/mp4
IHES
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.
Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation" of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.
2022-11-21T00:00:00+01:00
Slava Rychkov
dimensional reduction, random field Ising model, Parisi-Sourlas supersymmetry, dangerously irrelevant operator, epsilon-expansion, Researchers, Graduate Students
en
Slava Rychkov – Random Field Ising Model and Parisi-Sourlas Supersymmetry / 07/11/2022 - 21/11/2022
https://www.carmin.tv/uploads/video/video-a0d8b41f3675c83a3d606b63f1403560.jpg
oai:carmin.tv:scalar-curvature-rigidity-and-extremality-in-dimension-4
2022-11-18T00:14:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:scalar-curvature-rigidity-and-extremality-in-dimension-4
https://www.carmin.tv/fr/video/scalar-curvature-rigidity-and-extremality-in-dimension-4
Scalar curvature rigidity and extremality in dimension 4
video/mp4
IHES
In this talk, I will discuss the Finsler--Thorpe trick for curvature operators in dimension 4, and how it can be combined with twisted spinor methods to show that large classes of compact 4-manifolds, with or without boundary, with nonnegative sectional curvature are area-extremal for scalar curvature. These techniques also show that any region of positive sectional curvature on a 4-manifold is locally area-extremal. This is joint work with McFeely Jackson Goodman (UC Berkeley).
2022-11-11T00:00:00+01:00
Renato Bettiol
Researchers
en
https://www.carmin.tv/uploads/video/video-ad960eb2ccd27c8cb2df68b93335ae7b.jpg
oai:carmin.tv:scalar-curvature-rigidity
2022-11-18T00:18:01+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:scalar-curvature-rigidity
https://www.carmin.tv/fr/video/scalar-curvature-rigidity
Scalar curvature rigidity
video/mp4
IHES
Many manifolds are (positive) scalar curvature rigid: one can't increase the scalar curvature without shrinking the manifold. The first of these results was established by Llarull (for the round spheres), using spinorial techniques. We discuss the problem and the known solutions, including current research questions around this topic.
2022-11-11T00:00:00+01:00
Thomas Schick
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/video-d6f4e7899b274845ca742a49ccc0be32.jpg
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-3-4
2022-11-22T16:29:00+01:00
videos:institution:ihes
videos:collection:slava-rychkov-random-field-ising-model-and-parisi-sourlas-supersymmetry
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-3-4
https://www.carmin.tv/fr/video/random-field-ising-model-and-parisi-sourlas-supersymmetry-3-4
Random Field Ising Model and Parisi-Sourlas Supersymmetry (3/4)
video/mp4
IHES
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.
Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation" of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.
2022-11-16T00:00:00+01:00
Slava Rychkov
dimensional reduction, random field Ising model, Parisi-Sourlas supersymmetry, dangerously irrelevant operator, epsilon-expansion, Researchers, Graduate Students
en
Slava Rychkov – Random Field Ising Model and Parisi-Sourlas Supersymmetry / 07/11/2022 - 21/11/2022
https://www.carmin.tv/uploads/video/video-bd6ef1bdc12cc875d0332eb984ef11a7.jpg
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-2-4
2022-11-15T09:56:16+01:00
videos:institution:ihes
videos:collection:slava-rychkov-random-field-ising-model-and-parisi-sourlas-supersymmetry
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-2-4
https://www.carmin.tv/fr/video/random-field-ising-model-and-parisi-sourlas-supersymmetry-2-4
Random Field Ising Model and Parisi-Sourlas Supersymmetry (2/4)
video/mp4
IHES
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.
Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation" of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.
2022-11-14T00:00:00+01:00
Slava Rychkov
dimensional reduction, random field Ising model, Parisi-Sourlas supersymmetry, dangerously irrelevant operator, epsilon-expansion, Researchers, Graduate Students
en
Slava Rychkov – Random Field Ising Model and Parisi-Sourlas Supersymmetry / 07/11/2022 - 21/11/2022
https://www.carmin.tv/uploads/video/video-6807e6653204a0ec4fd9dfc1a5438bce.jpg
oai:carmin.tv:capacity-in-low-regularity-with-connections-to-general-relativity
2022-11-14T16:00:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:capacity-in-low-regularity-with-connections-to-general-relativity
https://www.carmin.tv/fr/video/capacity-in-low-regularity-with-connections-to-general-relativity
Capacity in low regularity, with connections to general relativity
video/mp4
IHES
The classical concept of capacity generalizes from Euclidean space to complete Riemannian manifolds, and even to suitable classes of metric spaces. I will discuss recent joint work with Raquel Perales and Jim Portegies on understanding capacity in local integral current spaces, describing the behavior of capacity when the background spaces converge in the pointed Sormani--Wenger intrinsic flat sense. Connections between the main results and the concept of total mass in general relativity will be discussed.
2022-10-28T00:00:00+02:00
Jeff Jauregui
Researchers, Graduate Students
en
https://www.carmin.tv/uploads/video/Jeff_Jauregui-c2615a970d166be447feaa09a0198033-video--df67f51d87847e3c7ca4a890be8b555b.jpg
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-1-4
2022-11-09T16:46:43+01:00
videos:institution:ihes
videos:collection:slava-rychkov-random-field-ising-model-and-parisi-sourlas-supersymmetry
oai:carmin.tv:random-field-ising-model-and-parisi-sourlas-supersymmetry-1-4
https://www.carmin.tv/fr/video/random-field-ising-model-and-parisi-sourlas-supersymmetry-1-4
Random Field Ising Model and Parisi-Sourlas Supersymmetry (1/4)
video/mp4
IHES
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.
Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation" of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.
2022-11-07T00:00:00+01:00
Mandarine Audiovisuel
Slava Rychkov
dimensional reduction, random field Ising model, Parisi-Sourlas supersymmetry, dangerously irrelevant operator, epsilon-expansion, Researchers, Graduate Students
en
Slava Rychkov – Random Field Ising Model and Parisi-Sourlas Supersymmetry / 07/11/2022 - 21/11/2022
https://www.carmin.tv/uploads/video/video-252ab981244a64668ce851a8c812adb6.jpg
oai:carmin.tv:recent-inequalities-on-the-mass-to-capacity-ratio
2022-11-03T10:06:02+01:00
videos:institution:ihes
videos:collection:not-only-scalar-curvature-seminar
oai:carmin.tv:recent-inequalities-on-the-mass-to-capacity-ratio
https://www.carmin.tv/fr/video/recent-inequalities-on-the-mass-to-capacity-ratio
Recent inequalities on the mass-to-capacity ratio
video/mp4
IHES
On an asymptotically flat 3-manifold, both the mass and the capacity have unit of length, and hence their ratio is a dimensionless quantity. In this talk, I will discuss recent work on establishing new inequalities for the mass-to-capacity ratio on manifolds with nonnegative scalar curvature. Besides revealing additional proofs of the positive mass theorem, applications of these inequalities include new sufficient conditions guaranteeing positive mass via $C^0$-geometry of regions separating the boundary and the infinity. If time permits, a proposal to study manifolds with the mass-to-capacity ratio bounded by one will also be discussed.
2022-10-28T00:00:00+02:00
Pengzi Miao
Researchers
en
https://www.carmin.tv/uploads/video/video-da3434b649618b7fd6e4397d4d25073c.jpg
oai:carmin.tv:language-origins-an-animal-communication-perspective
2022-08-04T12:00:38+02:00
videos:institution:ihes
videos:collection:secret-missives-a-journey-in-natural-communication
oai:carmin.tv:language-origins-an-animal-communication-perspective
https://www.carmin.tv/fr/video/language-origins-an-animal-communication-perspective
Language Origins: an Animal Communication Perspective
video/mp4
IHES
Human language is arguably the most complex communication system currently known, however, the origins of language remain surprisingly elusive. In this lecture, I will revisit this conundrum and illustrate how studying animal communication can provide a much-needed window into the evolutionary roots of language. I will specifically focus on what comparative data exists for syntax in animal vocal systems (i.e. the ability to combine meaningful vocalizations together into larger meaningful structures). Data from primates and birds suggests that this core property of language is not unique to humans but exists, in more simple forms, in animals. I will discuss the evolutionary implications of these findings for reconstructing the emergence of syntax and language more generally.
2022-06-28T00:00:00+02:00
Simon Townsend
General Public
en
Secret missives: a journey in natural communication / Spoken or written human languages embody communication between individuals and computer languages between man and machine. In a broader context, inter- and intra-species communication can span the senses. The aim of this meeting is to discuss the current knowledge and future perspectives of research on the diverse mechanisms and roles of communication across biological systems and within social organizations. / Yves Barral (ETH Zürich), Mikhail Gromov (IHES & New York University), Robert Penner (IHES & University of California Los Angeles), Vasily Pestun (IHES & IBM Research), Nicolas Minc (IJM, Université Paris Cité/CNRS) / 27/06/2022 - 30/06/2022 / https://indico.math.cnrs.fr/event/7182/page/521-lsc-2022-public-lectures
https://www.carmin.tv/uploads/video/video-2a75472a2414b57fe8fdab22f3fb162a.jpg
oai:carmin.tv:derived-aspects-of-the-langlands-program-2-3
2022-07-29T17:36:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:derived-aspects-of-the-langlands-program-2-3
https://www.carmin.tv/fr/video/derived-aspects-of-the-langlands-program-2-3
Derived Aspects of the Langlands Program (2/3)
video/mp4
IHES
We discuss ways in which derived structures have recently emerged in connection with the Langlands correspondence, with an emphasis on derived Galois deformation rings and derived Hecke algebras.
2022-07-29T00:00:00+02:00
Michael Harris
Tony Feng
motivic cohomology, derived deformation ring, derived Hecke algebra, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-a50623f0224c237f193da68be73b09f2.jpg
oai:carmin.tv:high-dimensional-gross-zagier-formula-2-2
2022-07-29T17:40:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:high-dimensional-gross-zagier-formula-2-2
https://www.carmin.tv/fr/video/high-dimensional-gross-zagier-formula-2-2
High-dimensional Gross–Zagier Formula (2/2)
video/mp4
IHES
I'll discuss various generalizations of the Gross--Zagier formula to high dimensional Shimura varieties, with an emphasis on the AGGP conjecture and the relative trace formula approach. Roughly the first lecture will be devoted to the global aspect and the second one to the local aspect.
2022-07-29T00:00:00+02:00
Wei Zhang
relative trace formula, Gross--Zagier formula, Arithmetic GGP conjecture, Arithmetic fundamental lemma and transfer, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-5be378b0b0485a0365d16e55c76ece11.jpg
oai:carmin.tv:local-and-global-questions-beyond-endoscopy-2-2
2022-07-29T18:36:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:local-and-global-questions-beyond-endoscopy-2-2
https://www.carmin.tv/fr/video/local-and-global-questions-beyond-endoscopy-2-2
Local and Global Questions “Beyond Endoscopy” (2/2)
video/mp4
IHES
The near-completion of the program of endoscopy poses the question of what lies next.
These talks will take a broad view of ideas beyond the program of endoscopy, highlighting the connections among them, and emphasizing the relationship between local and global aspects. Central among those ideas is the one proposed in a 2000 lecture of R.~P.~Langlands, aiming to extract from the stable trace formula of a group $G$ the bulk of those automorphic representations in the image of the conjectural functorial lift corresponding to a morphism of $L$-groups ${^LH}\to {^LG}$. With the extension of the problem of functoriality to the ``relative'' setting of spherical varieties and related spaces, some structure behind such comparisons has started to reveal itself. In a seemingly unrelated direction, a program initiated by Braverman--Kazhdan, also around 2000, to generalize the Godement--Jacquet proof of the functional equation to arbitrary $L$-functions, has received renewed attention in recent years. We survey ideas and developments in this direction, as well, and discuss the relationship between the two programs.
2022-07-29T00:00:00+02:00
Yiannis Sakellaridis
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-a415431ab0142e9062375df3d6c22deb.jpg
oai:carmin.tv:derived-aspects-of-the-langlands-program-3-3
2022-07-29T20:26:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:derived-aspects-of-the-langlands-program-3-3
https://www.carmin.tv/fr/video/derived-aspects-of-the-langlands-program-3-3
Derived Aspects of the Langlands Program (3/3)
video/mp4
IHES
We discuss ways in which derived structures have recently emerged in connection with the Langlands correspondence, with an emphasis on derived Galois deformation rings and derived Hecke algebras.
2022-07-29T00:00:00+02:00
Michael Harris
Tony Feng
motivic cohomology, derived deformation ring, derived Hecke algebra, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-66fba22f38896a7683cbc648d63220c5.jpg
oai:carmin.tv:derived-aspects-of-the-langlands-program-1-3
2022-07-29T10:34:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:derived-aspects-of-the-langlands-program-1-3
https://www.carmin.tv/fr/video/derived-aspects-of-the-langlands-program-1-3
Derived Aspects of the Langlands Program (1/3)
video/mp4
IHES
We discuss ways in which derived structures have recently emerged in connection with the Langlands correspondence, with an emphasis on derived Galois deformation rings and derived Hecke algebras.
2022-07-28T00:00:00+02:00
Michael Harris
Tony Feng
motivic cohomology, derived deformation ring, derived Hecke algebra, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-df4778fc411296757de3331c156649c8.jpg
oai:carmin.tv:local-and-global-questions-beyond-endoscopy-1-2
2022-07-29T10:38:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:local-and-global-questions-beyond-endoscopy-1-2
https://www.carmin.tv/fr/video/local-and-global-questions-beyond-endoscopy-1-2
Local and Global Questions “Beyond Endoscopy” (1/2)
video/mp4
IHES
The near-completion of the program of endoscopy poses the question of what lies next.
These talks will take a broad view of ideas beyond the program of endoscopy, highlighting the connections among them, and emphasizing the relationship between local and global aspects. Central among those ideas is the one proposed in a 2000 lecture of R.~P.~Langlands, aiming to extract from the stable trace formula of a group $G$ the bulk of those automorphic representations in the image of the conjectural functorial lift corresponding to a morphism of $L$-groups ${^LH}\to {^LG}$. With the extension of the problem of functoriality to the ``relative'' setting of spherical varieties and related spaces, some structure behind such comparisons has started to reveal itself. In a seemingly unrelated direction, a program initiated by Braverman--Kazhdan, also around 2000, to generalize the Godement--Jacquet proof of the functional equation to arbitrary $L$-functions, has received renewed attention in recent years. We survey ideas and developments in this direction, as well, and discuss the relationship between the two programs.
2022-07-28T00:00:00+02:00
Yiannis Sakellaridis
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-e2d680046dbb5c36d58a9cba2ada2f77.jpg
oai:carmin.tv:high-dimensional-gross-zagier-formula-1-2
2022-07-28T17:18:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:high-dimensional-gross-zagier-formula-1-2
https://www.carmin.tv/fr/video/high-dimensional-gross-zagier-formula-1-2
High-dimensional Gross–Zagier Formula (1/2)
video/mp4
IHES
I'll discuss various generalizations of the Gross--Zagier formula to high dimensional Shimura varieties, with an emphasis on the AGGP conjecture and the relative trace formula approach. Roughly the first lecture will be devoted to the global aspect and the second one to the local aspect.
2022-07-28T00:00:00+02:00
Wei Zhang
relative trace formula, Gross--Zagier formula, Arithmetic GGP conjecture, Arithmetic fundamental lemma and transfer, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-d3aba6a0e4c1b274679b6bd10c46603d.jpg
oai:carmin.tv:between-coherent-and-constructible-local-langlands-correspondences
2022-07-28T17:38:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:between-coherent-and-constructible-local-langlands-correspondences
https://www.carmin.tv/fr/video/between-coherent-and-constructible-local-langlands-correspondences
Between Coherent and Constructible Local Langlands Correspondences
video/mp4
IHES
(Joint with Harrison Chen, David Helm and David Nadler.)
Refined forms of the local Langlands correspondence seek to relate representations of reductive groups over local fields with sheaves on stacks of Langlands parameters. But what kind of sheaves? Conjectures in the spirit of Kazhdan-Lusztig theory describe representations of a group and its pure inner forms with fixed central character in terms of constructible sheaves. Conjectures in the spirit of geometric Langlands describe representations with varying central character of a large family of groups associated to isocrystals in terms of coherent sheaves. The latter conjectures also take place on a larger parameter space, in which Frobenius (or complex conjugation) is allowed a unipotent part.
In this talk we propose a general mechanism that interpolates between these two settings. This mechanism derives from the theory of cyclic homology, as interpreted through circle actions in derived algebraic geometry. We apply this perspective to categorical forms of the local Langlands conjectures for both archimedean and non-archimedean local fields. In the archimedean case, we explain a conjectural realization of coherent local Langlands as geometric Langlands on the twistor line, the real counterpart of the Fargues-Fontaine curve, and its relation to constructible local Langlands via circle actions. In the nonarchimedean case, we describe how circle actions relate coherent and constructible realizations of affine Hecke algebras and of all smooth representations of $GL_n$, and propose a mechanism to relate the two settings in general.
2022-07-28T00:00:00+02:00
David Ben-Zvi
coherent sheaves, derived algebraic geometry, cyclic homology, constructible sheaves, local Langlands correspondence, twistor line, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-4d9b97bb7998cac9a9972701860fddbb.jpg
oai:carmin.tv:geometric-and-arithmetic-theta-correspondences-2-2
2022-07-28T09:56:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:geometric-and-arithmetic-theta-correspondences-2-2
https://www.carmin.tv/fr/video/geometric-and-arithmetic-theta-correspondences-2-2
Geometric and Arithmetic Theta Correspondences (2/2)
video/mp4
IHES
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also known as the Kudla program) and their applications.
2022-07-27T00:00:00+02:00
Chao Li
Geometric theta lifting, arithmetic theta lifting, special cycles, derivative of Eisenstein series, derivative of L-functions, arithmetic theta functions, arithmetic Siegel-Weil formula, arithmetic inner product formula, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-058f2d1e1c132ade63b21433e2c85d59.jpg
oai:carmin.tv:shimura-varieties-and-modularity-3-3
2022-07-27T18:34:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:shimura-varieties-and-modularity-3-3
https://www.carmin.tv/fr/video/shimura-varieties-and-modularity-3-3
Shimura Varieties and Modularity (3/3)
video/mp4
IHES
We discuss vanishing theorems for the cohomology of Shimura varieties with torsion coefficients, under a genericity condition at an auxiliary prime. We describe two complementary approaches to these results, due to Caraiani-Scholze and Koshikawa, both of which rely on the geometry of the Hodge-Tate period morphism for the corresponding Shimura varieties. Finally, we explain how these vanishing results can be applied to local-global compatibility questions for the Galois representations constructed in the first lecture.
2022-07-27T00:00:00+02:00
Ana Caraiani
Sug Woo Shin
Galois representations, Shimura varieties, automorphic representations, locally symmetric spaces, modularity lifting, local-global compatibility of the Langlands correspondence, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-f643d24aa91b0fb366ddb262accdccea.jpg
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-3-3
2022-07-27T12:18:03+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-3-3
https://www.carmin.tv/fr/video/the-langlands-program-and-the-moduli-of-bundles-on-the-curve-3-3
The Langlands Program and the Moduli of Bundles on the Curve (3/3)
video/mp4
IHES
I will speak about my joint work about the geometrization of the local Langlands correspondence.
2022-07-26T00:00:00+02:00
Peter Scholze
Laurent Fargues
p-adic Hodge theory, p-adic geometry, Langlands program, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-1fde863214844f19eb899192294ae10f.jpg
oai:carmin.tv:shimura-varieties-and-modularity-2-3
2022-07-27T12:18:03+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:shimura-varieties-and-modularity-2-3
https://www.carmin.tv/fr/video/shimura-varieties-and-modularity-2-3
Shimura Varieties and Modularity (2/3)
video/mp4
IHES
We describe the Calegari-Geraghty method for proving modularity lifting theorems beyond the classical setting of the Taylor-Wiles method. We discuss the three conjectures that this method relies on (existence of Galois representations, local-global compatibility and vanishing of cohomology outside a certain range of degrees) and their current status, and then explain the commutative algebra underlying the method.
2022-07-26T00:00:00+02:00
Ana Caraiani
Sug Woo Shin
Galois representations, Shimura varieties, automorphic representations, locally symmetric spaces, modularity lifting, local-global compatibility of the Langlands correspondence, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-05a547c15f4694abf8f559f51aa19ef8.jpg
oai:carmin.tv:geometric-and-arithmetic-theta-correspondences-1-2
2022-07-27T12:20:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:geometric-and-arithmetic-theta-correspondences-1-2
https://www.carmin.tv/fr/video/geometric-and-arithmetic-theta-correspondences-1-2
Geometric and Arithmetic Theta Correspondences (1/2)
video/mp4
IHES
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also known as the Kudla program) and their applications.
2022-07-26T00:00:00+02:00
Chao Li
Geometric theta lifting, arithmetic theta lifting, special cycles, derivative of Eisenstein series, derivative of L-functions, arithmetic theta functions, arithmetic Siegel-Weil formula, arithmetic inner product formula, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-0d9eafff843e00b01d8b7bc4e048ff46.jpg
oai:carmin.tv:shimura-varieties-and-modularity-1-3
2022-07-26T17:18:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:shimura-varieties-and-modularity-1-3
https://www.carmin.tv/fr/video/shimura-varieties-and-modularity-1-3
Shimura Varieties and Modularity (1/3)
video/mp4
IHES
We describe the construction of Galois representations associated to regular algebraic cuspidal automorphic representations of GL_n over a CM field, as well as those Galois representations associated to torsion classes that occur in the Betti cohomology of the corresponding locally symmetric spaces. The emphasis will be on Scholze’s proof, which applies to torsion classes and which uses perfectoid Shimura varieties and the Hodge-Tate period morphism.
2022-07-26T00:00:00+02:00
Ana Caraiani
Sug Woo Shin
Galois representations, Shimura varieties, automorphic representations, locally symmetric spaces, modularity lifting, local-global compatibility of the Langlands correspondence, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-d3aec0b733261d478961416ace88c968.jpg
oai:carmin.tv:branching-laws-homological-aspects
2022-07-26T15:46:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:branching-laws-homological-aspects
https://www.carmin.tv/fr/video/branching-laws-homological-aspects
Branching laws: homological aspects
video/mp4
IHES
By this time in the summer school, the audience will have seen
the question about decomposing a representation of a group when restricted to a subgroup which is referred
to as the branching law. In this lecture, we focus attention on homological aspects of the branching law. The lecture will survey this topic beginning from the beginning going up to several results which have recently been proved.
2022-07-25T00:00:00+02:00
Dipendra Prasad
duality, representations of p-adic groups, branching laws, Homological methods, Ext, Euler-Poincare characteristic, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-3fe75ee5ce059ff96cb59668d57b438b.jpg
oai:carmin.tv:on-moduli-spaces-of-local-langlands-parameters-2-2
2022-07-26T15:50:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:on-moduli-spaces-of-local-langlands-parameters-2-2
https://www.carmin.tv/fr/video/on-moduli-spaces-of-local-langlands-parameters-2-2
On Moduli Spaces of Local Langlands Parameters (2/2)
video/mp4
IHES
The moduli space of local Langlands parameters plays a key role in the formulation of some recent enhancements of the original local Langlands correspondence, such as the "local Langlands correspondence in families" and various "categorifications/geometrizations of LLC". We will explain their construction and basic properties, with special emphasis on the coarse moduli spaces.
2022-07-25T00:00:00+02:00
Jean-François Dat
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-cb381a628dad0f74b899c2ddb2e41505.jpg
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-4-4
2022-07-26T17:45:33+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-4-4
https://www.carmin.tv/fr/video/an-introduction-to-the-categorical-p-adic-langlands-program-4-4
An Introduction to the Categorical p-adic Langlands Program (4/4)
video/mp4
IHES
An introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
2022-07-25T00:00:00+02:00
Matthew Emerton
Toby Gee
Eugen Hellman
Langlands, p-adic, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-74185915c24fd514f0269bdf9f787c12.jpg
oai:carmin.tv:supercuspidal-representations-construction-classification-and-characters-2-2
2022-07-25T17:54:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:supercuspidal-representations-construction-classification-and-characters-2-2
https://www.carmin.tv/fr/video/supercuspidal-representations-construction-classification-and-characters-2-2
Supercuspidal Representations: Construction, Classification, and Characters (2/2)
video/mp4
IHES
We have seen in the first week of the summer school that the buildings blocks for irreducible representations of p-adic groups are the supercuspidal representations. In these talks we will explore explicit exhaustive constructions of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations in the p-adic world and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat--Tits theory and Moy--Prasad filtration, which we will introduce in the lecture series.
2022-07-25T00:00:00+02:00
Jessica Fintzen
exhaustive construction of supercuspidal representations of p-adic groups, Harish-Chandra character formula, discrete series representations, Bruhat--Tits theory, Moy--Prasad filtration, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-789abb8b9705c254e1efbaa18140407b.jpg
oai:carmin.tv:supercuspidal-representations-construction-classification-and-characters-1-2
2022-07-24T14:16:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:supercuspidal-representations-construction-classification-and-characters-1-2
https://www.carmin.tv/fr/video/supercuspidal-representations-construction-classification-and-characters-1-2
Supercuspidal Representations: Construction, Classification, and Characters (1/2)
video/mp4
IHES
We have seen in the first week of the summer school that the buildings blocks for irreducible representations of p-adic groups are the supercuspidal representations. In these talks we will explore explicit exhaustive constructions of these supercuspidal representations and their character formulas and observe a striking parallel between a large class of these representations in the p-adic world and discrete series representations of real algebraic Lie groups. A key ingredient for the construction of supercuspidal representations is the Bruhat--Tits theory and Moy--Prasad filtration, which we will introduce in the lecture series.
2022-07-22T00:00:00+02:00
Jessica Fintzen
exhaustive construction of supercuspidal representations of p-adic groups, Harish-Chandra character formula, discrete series representations, Bruhat--Tits theory, Moy--Prasad filtration, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-5a361f9ae916b53d62f1fe7a60e7775a.jpg
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-2-3
2022-07-24T15:06:03+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-2-3
https://www.carmin.tv/fr/video/the-langlands-program-and-the-moduli-of-bundles-on-the-curve-2-3
The Langlands Program and the Moduli of Bundles on the Curve (2/3)
video/mp4
IHES
I will speak about my joint work about the geometrization of the local Langlands correspondence.
2022-07-22T00:00:00+02:00
Peter Scholze
Laurent Fargues
p-adic Hodge theory, p-adic geometry, Langlands program, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-0ee7948e53d88fb32ba6fc547c18f528.jpg
oai:carmin.tv:on-moduli-spaces-of-local-langlands-parameters-1-2
2022-07-22T13:28:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:on-moduli-spaces-of-local-langlands-parameters-1-2
https://www.carmin.tv/fr/video/on-moduli-spaces-of-local-langlands-parameters-1-2
On Moduli Spaces of Local Langlands Parameters (1/2)
video/mp4
IHES
The moduli space of local Langlands parameters plays a key role in the formulation of some recent enhancements of the original local Langlands correspondence, such as the "local Langlands correspondence in families" and various "categorifications/geometrizations of LLC". We will explain their construction and basic properties, with special emphasis on the coarse moduli spaces.
2022-07-22T00:00:00+02:00
Jean-François Dat
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-9c5912fe79354c7a74a246843a58275c.jpg
oai:carmin.tv:explicit-constructions-of-automorphic-forms-2-2
2022-07-22T15:28:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:explicit-constructions-of-automorphic-forms-2-2
https://www.carmin.tv/fr/video/explicit-constructions-of-automorphic-forms-2-2
Explicit Constructions of Automorphic Forms (2/2)
video/mp4
IHES
I will discuss the theory of theta correspondence, highlighting basic principles and recent results, before explaining how theta correspondence can now be viewed as part of the relative Langlands program.
I will then discuss other methods of construction of automorphic forms, such as automorphic descent and its variants and the generalized doubling method.
2022-07-22T00:00:00+02:00
Wee Teck Gan
theta correspondence, doubling method, quantization, automorphic descent, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-553e6382268239aa767ac795c2975814.jpg
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-3-4
2022-07-26T17:47:22+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-3-4
https://www.carmin.tv/fr/video/an-introduction-to-the-categorical-p-adic-langlands-program-3-4
An Introduction to the Categorical p-adic Langlands Program (3/4)
video/mp4
IHES
An introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
2022-07-21T00:00:00+02:00
Matthew Emerton
Toby Gee
Eugen Hellman
Langlands, p-adic, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-bef4c5015fb1a699a2fb32b5e9040b0b.jpg
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-1-3
2022-07-21T17:40:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:the-langlands-program-and-the-moduli-of-bundles-on-the-curve-1-3
https://www.carmin.tv/fr/video/the-langlands-program-and-the-moduli-of-bundles-on-the-curve-1-3
The Langlands Program and the Moduli of Bundles on the Curve (1/3)
video/mp4
IHES
I will speak about my joint work about the geometrization of the local Langlands correspondence.
2022-07-21T00:00:00+02:00
Peter Scholze
Laurent Fargues
p-adic Hodge theory, p-adic geometry, Langlands program, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-8c3c0750928e49898e35d37488e33294.jpg
oai:carmin.tv:explicit-constructions-of-automorphic-forms-1-2
2022-07-21T17:44:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:explicit-constructions-of-automorphic-forms-1-2
https://www.carmin.tv/fr/video/explicit-constructions-of-automorphic-forms-1-2
Explicit Constructions of Automorphic Forms (1/2)
video/mp4
IHES
I will discuss the theory of theta correspondence, highlighting basic principles and recent results, before explaining how theta correspondence can now be viewed as part of the relative Langlands program.
I will then discuss other methods of construction of automorphic forms, such as automorphic descent and its variants and the generalized doubling method.
2022-07-21T00:00:00+02:00
Wee Teck Gan
theta correspondence, doubling method, quantization, automorphic descent, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-28495632fdad4dd861ef9e5bb1ce9160.jpg
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-2-4
2022-07-26T17:47:29+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-2-4
https://www.carmin.tv/fr/video/an-introduction-to-the-categorical-p-adic-langlands-program-2-4
An Introduction to the Categorical p-adic Langlands Program (2/4)
video/mp4
IHES
An introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
2022-07-21T00:00:00+02:00
Matthew Emerton
Toby Gee
Eugen Hellman
Langlands, p-adic, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-33d6b352d3a075ad912b3ae667f506a8.jpg
oai:carmin.tv:what-does-geometric-langlands-mean-to-a-number-theorist-1-2
2022-07-21T14:26:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:what-does-geometric-langlands-mean-to-a-number-theorist-1-2
https://www.carmin.tv/fr/video/what-does-geometric-langlands-mean-to-a-number-theorist-1-2
What does geometric Langlands mean to a number theorist? (1/2)
video/mp4
IHES
2022-07-20T00:00:00+02:00
Sam Raskin
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-5367f79faf7ae9479fd06cbd76f221a3.jpg
oai:carmin.tv:what-does-geometric-langlands-mean-to-a-number-theorist-2-2
2022-07-21T14:30:03+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:what-does-geometric-langlands-mean-to-a-number-theorist-2-2
https://www.carmin.tv/fr/video/what-does-geometric-langlands-mean-to-a-number-theorist-2-2
What does geometric Langlands mean to a number theorist? (2/2)
video/mp4
IHES
2022-07-20T00:00:00+02:00
Sam Raskin
Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-1c597c3348960469125e020ca138a981.jpg
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-1-4
2022-07-26T17:47:35+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:an-introduction-to-the-categorical-p-adic-langlands-program-1-4
https://www.carmin.tv/fr/video/an-introduction-to-the-categorical-p-adic-langlands-program-1-4
An Introduction to the Categorical p-adic Langlands Program (1/4)
video/mp4
IHES
An introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
2022-07-20T00:00:00+02:00
Matthew Emerton
Toby Gee
Eugen Hellman
Langlands, p-adic, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-a6a0ae5f5c091ec12903a6d12bc699fd.jpg
oai:carmin.tv:orbital-integrals-moduli-spaces-and-invariant-theory-3-3
2022-07-20T23:54:01+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:orbital-integrals-moduli-spaces-and-invariant-theory-3-3
https://www.carmin.tv/fr/video/orbital-integrals-moduli-spaces-and-invariant-theory-3-3
Orbital integrals, moduli spaces and invariant theory (3/3)
video/mp4
IHES
The goal of these lectures is to sketch a general framework to study orbital integrals over equal characteristic local fields by means of moduli spaces of Hitchin type following the main lines of the proof of the fundamental lemma for Lie algebras. After recalling basic elements of the proof of the fundamental lemma for Lie algebras as well as recent related developments, I will explain an invariant theoretic construction which should a basic tool to understand general orbital integrals.
2022-07-20T00:00:00+02:00
Bao Chau Ngo
orbital integrals, moduli spaces, invariant theory, Hitchin fibration, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-bbd9d09921e5b559d261bfd07a5ee868.jpg
oai:carmin.tv:cohomology-sheaves-of-stacks-of-shtukas-2-2
2022-07-20T14:06:02+02:00
videos:institution:ihes
videos:collection:summer-school-on-the-langlands-program
oai:carmin.tv:cohomology-sheaves-of-stacks-of-shtukas-2-2
https://www.carmin.tv/fr/video/cohomology-sheaves-of-stacks-of-shtukas-2-2
Cohomology Sheaves of Stacks of Shtukas (2/2)
video/mp4
IHES
Cohomology sheaves and cohomology groups of stacks of shtukas are used in the Langlands program for function fields. We will explain (1) how the Eichler-Shimura relations imply the finiteness property of the cohomology groups, (2) how the finiteness and Drinfeld's lemma imply the action of the Weil group of the function field on the cohomology groups, and (3) how this action and the "Zorro lemma" imply the smoothness of the cohomology sheaves. The smoothness will be used in Sam Raskin’s lecture.
2022-07-19T00:00:00+02:00
Cong Xue
Smoothness, cohomology of stacks of shtukas, finiteness, Weil group, Researchers, Graduate Students
en
Summer School on the Langlands Program / It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.
Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.
The summer school will attempt to bring these exciting new directions together and explore their interactions. / Pierre-Henri Chaudouard, Wee Teck Gan, Tasho Kaletha, Yiannis Sakellaridis / 11/07/2022 - 29/07/2022 / https://indico.math.cnrs.fr/event/6909/
https://www.carmin.tv/uploads/video/video-31d60a27e93cdacbcba6aafc7258c498.jpg
eyJwYWdlIjoxLCJzZXQiOiJ2aWRlb3M6aW5zdGl0dXRpb246aWhlcyIsIm1ldGFkYXRhUHJlZml4Ijoib2FpX2RjIn0=