Math 276 (Topics in Topology): Atiyah‑Singer Index Theorem

Instructor:

Peter Teichner

Lectures:

Tuesday and Thursday, 12:30–2 in 51 Evans Hall

Lecture notes:

Dmitri Pavlov

Please report all typos in the lecture notes to me by email (pavlov at math).

Lecture notes: TeX, DVI, PostScript, PDF.

Homework 1: TeX, DVI, PostScript, PDF.

Homework 2: TeX, DVI, PostScript, PDF.

Homework 3: TeX, DVI, PostScript, PDF.

Homework 4: TeX, DVI, PostScript, PDF.

Mini-conference: Monday, May 16, 10–1 and 2–6, 740 Evans Hall. Dinner at 7.

Talks:

• 10–10:20: History of the index theorem (Santiago Canez)
• 10:30–10:50: (Harold Williams)
• 11–11:20: Riemann-Roch for elliptic curves (Aaron Mazel-Gee)
• 11:30–11:50: Index theorem for manifolds with boundary (Zachary Sylvan)
• 12:30–12:50: Applications of G-signature theorem to number theory (Eric Peterson)
• 2–2:50: Dirac operators and Weyl's asymptotics for their eigenvalues (Dan Berwick Evans and Nate Watson)
• 3–3:50: Geometric vanishing theorems (Dmitri Pavlov and Sebastian Hurtado-Salazar)
• 4:30–4:50: Positive mass conjecture in general relativity (Renato Vianna)
• 5–5:20: Grothendieck-Riemann-Roch (Yuhao Huang)
• 5:30–5:50: Twisted K-theory and the index theorem (Dario Beraldo)

References:

• Michael Atiyah, Isadore Singer: The index of elliptic operators: I
• Michael Atiyah, Graeme Segal: The index of elliptic operators: II
• Michael Atiyah, Isadore Singer: The index of elliptic operators: III
• Michael Atiyah, Isadore Singer: The index of elliptic operators: IV
• Michael Atiyah, Isadore Singer: The index of elliptic operators: V
• Friedrich Hirzebruch: Topological methods in algebraic geometry
• John Roe: Elliptic operators, topology and asymptotic methods
• Nicole Berline, Ezra Getzler, Michèle Vergne: Heat kernels and Dirac operators
• H. Blaine Lawson, Marie-Louise Michelsohn: Spin Geometry