Explore a proof of a stable algebraic version of Gromov's angle shrinking problem and its application to the dihedral rigidity conjecture in this 51-minute lecture. Delve into the computation of the Fredholm index of Dirac type operators on manifolds with polyhedral boundary. Learn about the joint work of Jinming Wang, Zhizhang Xie, and Guoliang Yu as presented by Jinming Wang from Texas A&M University at the Institut des Hautes Etudes Scientifiques (IHES).