A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1

Explore a 52-minute lecture on Gromov's angle shrinking problem and its role in proving Gromov's dihedral extremality/rigidity conjecture. Delve into the development of a new index theorem for manifolds with polyhedral boundary, focusing on the computation of the Fredholm index of a Dirac type operator. Discover a key deformation technique that simplifies the index computation, relying on a stable and algebraic version of Gromov's angle shrinking problem. Learn how this modified version of the problem contributes to the proof of the index theorem. Gain insights from the joint work of Zhizhang Xie, Jinmin Wang, and Guoliang Yu, presented by Zhizhang Xie from Texas A&M University at the Institut des Hautes Etudes Scientifiques (IHES).