Index Theory and Applications to Scalar Curvature

Explore index theory and its applications to scalar curvature geometry in this 49-minute lecture by Christian Bär from the University of Potsdam. Delve into two important index theorems for compact manifolds with boundary. Examine the first theorem, which calculates the index of a specific boundary value problem for a Dirac operator using the Euler number of the manifold. Investigate the second theorem, which connects the index of a boundary value problem to the index of an operator on the boundary. Discover how these theorems, particularly the second one, are applied to scalar curvature geometry. Learn about the collaborative research behind these findings, conducted with Simon Brendle, Bernhard Hanke, and Yipeng Wang. Gain insights into how the first index theorem relates to Yipeng Wang's subsequent talk in this series.