Math392C: Index Theory

Announcements

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

Schedule

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

Problem Sets

Problem Set #1

Problem Set #2

Problem Set #3

Readings

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.