Gromov's Rigidity Theorem for Polytopes with Acute Angles
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore a 59-minute lecture on Gromov's rigidity theorem for polytopes with acute angles, presented by Yipeng Wang from Columbia University at the Institut des Hautes Etudes Scientifiques (IHES). Delve into Gromov's conjecture on the scalar curvature extremality property of convex polytopes and learn about S. Brendle's recent proof using Dirac operator techniques and a smoothing construction. Examine Gromov's outlined proof for cases with acute dihedral angles and discover recent developments in the dihedral rigidity problem. Gain insights into the joint work of S. Brendle and Y. Wang, which introduces an alternative smoothing construction for Gromov's argument. Understand how their proof of the rigidity statement relies on a deep estimate by Fefferman and Phong. Reference the arXiv paper "On Gromov's rigidity theorem for polytopes with acute angles" for further study.
Syllabus
Yipeng Wang - On Gromov’s rigidity theorem for polytopes with acute angles
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
Notions of Scalar Curvature - Mikhail GromovInstitute for Advanced Study via YouTube Canonical Kaehler Metrics and Stability of Algebraic Varieties
International Mathematical Union via YouTube Curvature of the Determinant Line Bundle for Noncommutative Tori
Hausdorff Center for Mathematics via YouTube Static Black Hole Uniqueness Theorems - Lecture 3
ICTP Mathematics via YouTube Some Geometric Properties of Spacetime - Lecture 2
ICTP Mathematics via YouTube