Atiyah-Singer Seminar

(figure out the acronym yourself)



What: Atiyah-Singer Seminar
When: Mondays 2:45-3:45pm, starting Sept. 3, 2009
Where: Math 528


Literature:
[AS0] Atiyah and Singer, "The index of elliptic operators on compact manifolds"
[AS1] Atiyah and Singer, "The index of elliptic operators I"
[AS2] Atiyah and Segal, "The index of elliptic operators II"
[AS3] Atiyah and Singer, "The index of elliptic operators III"
[AS4] Atiyah and Singer, "The index of elliptic operators IV"
[AS5] Atiyah and Singer, "The idnex of elliptic operators V"
[S] Segal, "Equivariant K-theory"
[G] Gel'fand, "On elliptic equations"
[LM] Lawson and Michelsohn, Spin Geometry
[A] Atiyah, K-theory
[H] Hatcher, Vector Bundles and K-Theory
[BGV] Berline, Getzler, and Vergne, Heat Kernels and Dirac Operators
[ABS] Atiyah, Bott, and Shapiro, "Clifford modules"


Talks:
9/3 History; organizational meeting Alex
9/14 and 9/21 Equivariant K-theory [S], [A], [VBKT], [LM], [AS1] sec. 2 Zach Zach's notes
9/28 NO SEMINAR (Yom Kippur)
10/5 and 10/12 Index functions and the topological index [AS1] secs. 3-4, [LM] Thomas
10/19 Pseudodifferential operators and the analytical index [AS1] secs. 5-6, [LM] Adam
11/2 Digression on elliptic complexes; verification of the axioms for a-ind [AS1] secs. 7-9, [LM] Daniel
11/9 and 11/23 Relation to fixed-point sets and the Lefschetz theorem [AS2] Alex
11/30
2:15-3:45 		Passage to cohomology; lots of examples [AS3], [LM] Andre
Wed. 12/9 The heat kernel approach [BGV] Max Lipyanskiy
Jan. 2010 Dirac operators You


Other possible topics: families of operators ([AS4], [LM])), real operators ([AS5], [LM]), heat index proof (Atiyah-Bott-Patodi paper, Getzler papers, [LM]), supersymmetry (Witten paper), noncompact manifolds and discrete series of semisimple Lie groups (Atiyah paper, Atiyah-Schmid paper)


Contact Alex if you have questions.