YoVDO

Scalar Curvature Rigidity of Polytopes

Offered By: Centre de recherches mathématiques - CRM via YouTube

Tags

Differential Geometry Courses Harmonic Analysis Courses Manifolds Courses Polytopes Courses Riemannian Geometry Courses Scalar Curvature Courses Dirac Operator Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore a captivating lecture on the scalar curvature rigidity of polytopes, delivered by Simon Brendle as part of the Aisenstadt Chair Lecture Series. Delve into the fascinating world of differential geometry, focusing on Riemannian metrics and curvature positivity conditions. Discover Gromov's proposed comparison principle for polytopes with nonnegative scalar curvature, inspired by Toponogov's triangle comparison theorem. Learn about a recent result verifying Gromov's conjecture under stronger hypotheses, utilizing Fredholm theory for Dirac operators on manifolds with boundary and a harmonic analysis estimate by Fefferman and Phong. Gain insights into this central theme in differential geometry and its implications for understanding the properties of polytopes and manifolds.

Syllabus

Simon Brendle: Scalar curvature rigidity of polytopes


Taught by

Centre de recherches mathématiques - CRM

Related Courses

Geometry of 2-Dimensional Riemannian Disks and Spheres - Regina Rotman
Institute for Advanced Study via YouTube
Discrete Homotopy Theory and Applications
Applied Algebraic Topology Network via YouTube
Geodesic Complexity of Riemannian Manifolds
Applied Algebraic Topology Network via YouTube
The Gromov-Hausdorff Distance Between Spheres
Applied Algebraic Topology Network via YouTube
Symmetric Spaces by Pralay Chatterjee
International Centre for Theoretical Sciences via YouTube