Math392C: Index Theory


I posted a short handout containing a useful estimate.

No class on March 7.

We will have an extra session on Tuesday, March 20, at 5:00.

Basic Information

Professor: Dan Freed

Class Meetings: W 4:00-7:00, RLM 9.166

Discusion/Office Hours: Mondays, 2:30-4:00, RLM 9.162

For more details, see the First Day Handout


Chapter/Topic Students Date
2. Connections and characteristic classes Riccardo Pedrotti January 24
George Torres
3. Clifford algebras and Dirac operators Ivan Tulli January 31
Ricky Wedeen
4. Spin groups Arun Debray February 7
Sebastian Schulz
5. Analytic properties of Dirac operators Kendric Schafers February 14
Gillian Grindstaff
6. Hodge theory Adrian Clough February 21
Rok Gregoric
Qianyu Hao
7. Heat and wave equations Cameron Darwin February 28
Ravi Mohan
8. Traces and eigenvalue asymptotics Kenny Schefers March 21
Ivan Tulli
9. Some non-compact manifolds Sebastian Schulz March 28
Arun Debray
10. The Lefschetz formula George Torres April 4
Riccardo Pedrotti
11. The index problem Ricky Wedeen April 11
Rok Gregoric
12. The Getzler calculus and the local index theorem Cameron Darwin April 25
Ravi Mohan
13. Applications of the index theorem Ivan Tulli May 2
Kenny Schefers
14. Witten's approach to Morse theory Gillian Grindstaff May 7 (1:00, RLM 10.176)
Ricky Wedeen

Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3


Very old course notes on Dirac operators

Short essay on Atiyah-Singer index theorem by Higson-Roe (from Princeton Companion)

Announcement by Atiyah-Singer of index theorem

On elliptic equations by Gelfand

Proof of the spectral theorem for compact self-adjoint operators

An inequality important for the analysis of the Dirac operator and associated heat and wave operators

Mark Kac's article "Can you hear the shape of a drum?"

Atiyah-Bott papers (Part 1, Part 2) on the Lefschetz formula

Some Atiyah-Singer papers (Part 1, Part 3) on the index theorem

Getzler's papers (1 and 2) on the index theorem.

Witten paper on Morse theory and supersymmetry

Two papers by Bott (Paper 1, Paper 2) on Morse theory.