1 April 2022
Geometry and Topology: A Tale of Rigidity
A mainstream in mathematics is to study the relation between the geometry and topology of a manifold. The geometry is about the distance, length, area, volume and determined by its curvature. The topology is about properties that are preserved under continuous deformations. It is generally observed that a suitable assumption on the geometry would lead to certain restrictions on the topology. In this talk, we’ll discuss some recent progress in this direction, particularly the joint work with Xiaodong Cao and Matthew Gursky leading to a resolution of a conjecture proposed by S. Nishikawa.