Speaker: Prof. Fadil Santosa, School of Mathematics, University of Minnesota and Institute for Mathematics and its Applications
Title: The Mathematics behind Bar Codes
Subject: Rigidity theorems have a long history in Riemannian geometry. For example, long ago it was shown that the only convex body in Euclidean 3-space with spherical 'intrinsic boundary' must be the unit ball. The proofs of the classical rigidity theorems, however, do not seem to generalize to 'almost-rigidity' theorems: new techniques are required. In this talk, we will identify a few classical theorems regarding the rigidity of isometric immersions, and show how they can be turned into 'stability theorems' within the class of Riemannian 3-manifolds with boundary.