Atiyah-Singer Index Theorem

Seminar on the Atiyah-Singer index theorem, UT Austin 2013

These are the notes from a seminar on the Atiyah-Singer index theorem I organised at UT Austin in 2013:

  1. Characteristic classes (Lee Cohn) (pdf)
  2. Clifford algebras and Dirac operators (Tom Mainiero) (pdf)
  3. Spin groups I (Aaron Fenyes) (pdf)
  4. Spin groups II (Richard Derryberry) (pdf)
  5. Analysis of Dirac operators (Andrew Lee) (pdf)
  6. Hodge theory (Rustam Antia & Javier Morales) (pdf)
  7. Spin groups III (Rahul Shah) (pdf)
  8. The heat and wave equations (Valentin Zakharevich) (pdf)
  9. Traces and eigenvalue asymptotics (Cagri Karakurt) (pdf)
  10. The harmonic oscillator and non-compact manifolds (Richard Derryberry) (pdf)
  11. The Lefschetz formula (Laura Starkson) (pdf)
  12. The index problem (Valentin Zakharevich) (pdf)
  13. The Getzler calculus (Richard Derryberry) (pdf)
  14. The index theorem (Valentin Zakharevich) (pdf)
  15. Hirzebruch-Riemann-Roch (Lee Cohn) (pdf)