Triangles, Rotation, a Theorem and the Jackpot

TL;DR

This paper introduces undergraduates to the Atiyah-Singer index theorem, explaining its motivation, statement, and proof outline, and discusses applications like lattice point counting and knot concordance.

Contribution

It provides an accessible exposition of the Atiyah-Singer index theorem with applications, aimed at undergraduate learners.

Findings

Illustrates the theorem's connection to lattice point counting

Demonstrates applications in knot concordance

Provides an outline of the heat equation proof

Abstract

This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.