Deformations of Dirac operators
Deformations of Dirac operators have played important roles in various aspects in geometry and topology. In this expository talk I will discuss some of these applications.
Mathematics
and Interactions
Information about the video
- Date of recording 08/04/2022
- Date of publication 19/04/2022
- Institution IHES
- Licence CC BY-NC-ND
- Language English
- Audience Researchers, Graduate Students
- Format MP4
Domain(s)
Last related questions on MathOverflow
You have to connect your Carmin.tv account with mathoverflow to add questionAsk a question on MathOverflow
-
All the collection videos
![Scalar and mean curvature comparison via the Dirac operator]()
01:02:05published on February 3, 2022Scalar and mean curvature comparison via the Dirac operator
By Rudolf Zeidler
![Sequences of manifolds with lower bounds on their scalar curvature]()
49:31published on February 25, 2022Sequences of manifolds with lower bounds on their scalar curvature
By Christina Sormani
![Some introductory remarks on the Novikov conjecture]()
49:38published on February 22, 2022Some introductory remarks on the Novikov conjecture
By Shmuel Weinberger
![Rigidity theorems for the diffeomorphism action on spaces of metrics of positive scalar curvature]()
54:54published on March 11, 2022Rigidity theorems for the diffeomorphism action on spaces of metrics of positive scalar curvature
By Johannes Ebert
![Lower scalar curvature bounds for $C^0$ metrics: a Ricci flow approach]()
52:49published on March 25, 2022Lower scalar curvature bounds for $C^0$ metrics: a Ricci flow approach
By Paula Burkhardt-Guim
![Gromov’s dihedral rigidity conjecture and index theory on manifolds with corners]()
59:42published on April 7, 2022Gromov’s dihedral rigidity conjecture and index theory on manifolds with corners
By Jinming Wang
![Comparison of scalar curvature, mean curvature and dihedral angles, and their applications]()
01:01:04published on April 7, 2022Comparison of scalar curvature, mean curvature and dihedral angles, and their applications
By Zhizhang Xie
![Nonnegative scalar curvature and area decreasing maps on complete foliated manifolds]()
43:37published on April 21, 2022Nonnegative scalar curvature and area decreasing maps on complete foliated manifolds
By Guangxiang Su
![Incompressible hypersurface, positive scalar curvature and positive mass theorem]()
01:03:49published on May 3, 2022Incompressible hypersurface, positive scalar curvature and positive mass theorem
By Jintian Zhu
![Distance estimates in the spin setting and the positive mass theorem]()
01:04:17published on May 11, 2022Distance estimates in the spin setting and the positive mass theorem
By Simone Cecchini
![Yamabe constants, Yamabe invariants, and Gromov-Lawson surgeries]()
48:01published on May 24, 2022Yamabe constants, Yamabe invariants, and Gromov-Lawson surgeries
By Bernd Ammann
![Yamabe invariants, Weyl curvature, and the differential topology of 4-manifolds]()
01:10:21published on May 24, 2022Yamabe invariants, Weyl curvature, and the differential topology of 4-manifolds
By Claude LeBrun
![Level set methods for scalar curvature on three-manifolds]()
47:22published on June 30, 2022Level set methods for scalar curvature on three-manifolds
By Daniel Stern
![Capacity in low regularity, with connections to general relativity]()
59:15published on November 14, 2022Capacity in low regularity, with connections to general relativity
By Jeff Jauregui
![Scalar curvature rigidity and extremality in dimension 4]()
45:55published on November 17, 2022Scalar curvature rigidity and extremality in dimension 4
By Renato Bettiol
![Self-similar solutions to extension and approximation problems]()
57:53published on December 30, 2022Self-similar solutions to extension and approximation problems
By Robert Young
![Currents on metric spaces and intrinsic flat convergence]()
55:22published on February 10, 2023Currents on metric spaces and intrinsic flat convergence
By Christina Sormani
![Recent developments in constant mean curvature hypersurfaces I]()
47:01published on February 21, 2023Recent developments in constant mean curvature hypersurfaces I
By Xin Zhou
![Recent developments in constant mean curvature hypersurfaces II]()
51:23published on February 21, 2023Recent developments in constant mean curvature hypersurfaces II
By Liam Mazurowski
![Interplay between notions of convexity in complex, symplectic and contact geometries]()
01:02:35published on March 28, 2023Interplay between notions of convexity in complex, symplectic and contact geometries
By Yakov Eliashberg
![The completion of the space of Lagrangian submanifolds for the spectral metric]()
48:07published on April 27, 2023The completion of the space of Lagrangian submanifolds for the spectral metric
By Claude Viterbo
![A higher dimensional generalization of the Birkhoff attractor]()
59:02published on April 27, 2023A higher dimensional generalization of the Birkhoff attractor
By Vincent Humilière
![Positive mass theorem for asymptocially hyperbolic manifolds]()
51:59published on May 31, 2023Positive mass theorem for asymptocially hyperbolic manifolds
By Lan-Hsuan Huang
![Intrinsic flat stability of the positive mass theorem for graphical manifolds]()
53:07published on May 31, 2023Intrinsic flat stability of the positive mass theorem for graphical manifolds
By Raquel Perales
![Smoothing by Ricci-DeTurck flow and applications to scalar curvature]()
01:11:26published on June 13, 2023Smoothing by Ricci-DeTurck flow and applications to scalar curvature
By Man-Chun Lee
![On Gromov’s rigidity theorem for polytopes with acute angles]()
58:32published on November 14, 2023On Gromov’s rigidity theorem for polytopes with acute angles
By Yipeng Wang
![Intrinsic flat stability of Llarull’s theorem in dimension three]()
55:50published on November 14, 2023Intrinsic flat stability of Llarull’s theorem in dimension three
By Brian Allen
![Ricci curvature, fundamental group and the Milnor conjecture (I)]()
44:50published on December 5, 2023Ricci curvature, fundamental group and the Milnor conjecture (I)
By Aaron Naber
![Ricci curvature, fundamental group and the Milnor conjecture (II)]()
57:06published on December 5, 2023Ricci curvature, fundamental group and the Milnor conjecture (II)
By Daniele Semola
![Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension]()
01:00:32published on December 15, 2023Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension
By Jiayin Pan
![Generic regularity for minimizing hypersurfaces in 9 and 10 dimensions]()
48:55published on February 2, 2024Generic regularity for minimizing hypersurfaces in 9 and 10 dimensions
By Otis Chodosh
![A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part II)]()
50:52published on February 28, 2024A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part II)
By Jinming Wang
![A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part I)]()
51:39published on February 28, 2024A stable version of Gromov’s angle-shrinking problem and its index theoretic applications (Part I)
By Zhizhang Xie
![Positive mass theorem for asymptotically flat manifolds with isolated conical singularities]()
44:30published on April 24, 2024Positive mass theorem for asymptotically flat manifolds with isolated conical singularities
By Changliang Wang
![Positive mass theorem and positive scalar curvature in the presence of a singularity]()
48:20published on April 24, 2024Positive mass theorem and positive scalar curvature in the presence of a singularity
By Xianzhe Dai
![Geometric variational methods to (not only) scalar curvature problems]()
48:32published on May 9, 2024Geometric variational methods to (not only) scalar curvature problems
By Chao Li
![On spectra of Laplace and Dirac operators on noncompact manifolds]()
46:03published on May 28, 2024On spectra of Laplace and Dirac operators on noncompact manifolds
By Nadine Große
![Width, scalar curvature and macroscopic scalar curvature]()
38:42published on June 3, 2024Width, scalar curvature and macroscopic scalar curvature
By Yevgeny Liokumovich
![Dimension-independent functional inequalities on sub-Riemannian manifolds]()
58:19published on June 18, 2024Dimension-independent functional inequalities on sub-Riemannian manifolds
By Masha Gordina
![Rigidity results for initial data sets satisfying the dominant energy condition]()
01:03:08published on December 4, 2024Rigidity results for initial data sets satisfying the dominant energy condition
By Tsz-Kiu Aaron Chow
![How to define an inverse mean curvature flow coming out of crystals?]()
01:12:26published on March 31, 2025How to define an inverse mean curvature flow coming out of crystals?
By Esther Cabezas-Rivas
![Complete Riemannian 4-manifolds with uniformly positive scalar curvature metric]()
01:03:18published on April 14, 2025Complete Riemannian 4-manifolds with uniformly positive scalar curvature metric
By Anubhav Mukherjee
-
Suggestions
![Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1]()
01:32:03published on April 25, 2025Ergodic theory of the geodesic flow of hyperbolic surfaces - Lecture 1
By Barbara Schapira
Register
- Bookmark videos
- Add videos to see later &
keep your browsing history - Comment with the scientific
community - Get notification updates
for your favorite subjects
