What is … the Atiyah-Singer Index Theorem?

This page hosts information on Lucas Braune's talk "What is … the Atiyah-Singer Index Theorem?" at the "What is …?" seminar. The talk will take place on Friday, June 27, 4:00pm at HU, RUD 25 1.023.

Abstract

The Atiyah-Singer index theorem is a general result that gives an integral formula for the index of an elliptic operator on a compact manifold. It has as immediate corollaries, fundamental theorems in different areas of geometry --- theorems whose statements have seemingly nothing to do with an index. The main examples are the Chern-Gauss-Bonnet theorem, the Hirzebruch signature formula, and the Riemann-Roch-Hirzebruch theorem. My purpose for this talk is to show each of these theorems as a solution to an index problem and, with this as the motivation, to explain the statement of a version of the Atiyah-Singer index theorem.

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