STARLIGHT
THEORY

Index Theory and the Atiyah-Singer Theorem

Index Theory: Connecting Analysis and Topology

The Atiyah-Singer index theorem represents one of the most significant achievements in 20th-century mathematics, connecting seemingly disparate areas of mathematics in a profound way.

The Power of Index Theory

Index theory provides a bridge between:

  • Analytical properties of differential operators
  • Topological invariants of manifolds
  • Geometric structures
  • K-theory

Main Topics:

  1. Elliptic operators
  2. The analytical index
  3. The topological index
  4. K-theory and characteristic classes
  5. Applications to geometry and physics

This theory has led to breakthroughs in:

  • Gauge theory
  • String theory
  • Quantum field theory
  • Geometric quantization

Join us as we explore this crowning achievement of modern mathematics!