Your course mark will be based on two items:

- regular attendance

- an essay on some topic related to the theme of this course.

The essay should be around 3-4 pages, preferably typed. You can pick one of the topics below, or also suggest a topic yourself. It might be on some "standard" material that wasn't discussed in class, or also a summary of some research paper.

Please let me know your choice by October 31. (Just for organizational purposes -- this doesn't have to be final.) The essay is due by December 7, i.e. the last day of classes.

Topics:

  • The Spin-c Dirac operator
  • The index theorem for foliations
  • The index theorem for manifolds with boundary
  • The heat kernel approach to the index theorem
  • The cobordism approach to the index theorem
  • The Hirzebruch-Riemann-Roch theorem
  • The Atiyah-Bott Lefschetz formula
  • The equivariant index theorem
  • Applications of the index theorem