Hi all.  Here is a PRELIMINARY schedule of student class presentations and so on, for the rest of the semester.  I will try to update as we go along.

November 4th – Damien – Families index and Bott periodicity

November 11th and 13th (I will be away) – David and Jinpeng – Characteristic classes and genera

December 2 – Alok (Vector fields on manifolds) AND Angel (Elliptic operators on homogeneous spaces)

December 9 – Qijun – Analytic K-homology

References

Atiyah, M. F., and I. M. Singer. 1971. “The Index of Elliptic Operators: IV.” The Annals of Mathematics, Second Series, 93 (1): 119–38. (section 1)

Atiyah, M.F. 1968. “Bott Periodicity and the Index of Elliptic Operators.” Oxford Quarterly Journal of Mathematics 19: 113–40.

Atiyah, M. F., and I. M. Singer. 1968. “The Index of Elliptic Operators: III.” The Annals of Mathematics, Second Series, 87 (3): 546–604. (Sections 1 and 2)

Milnor, J.W., and J.D. Stasheff. 1974. Characteristic Classes. Vol. 76. Annals of Mathematics Studies. Princeton University Press, Princeton, N.J.

Atiyah, M.F. 1970. “Vector Fields on Manifolds.” Arbeitsgemeinschaft Für Forschung Des Landes Nordrhein Westfalen 200: 7–24.

Bott, R. 1965. “The Index Theorem for Homogeneous Differential Operators.” In Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse, edited by S.S. Cairns, 167–86. Princeton University Press, Princeton, N.J.

Atiyah, M.F. 1969. “Global Theory of Elliptic Operators.” In Proceedings of the International Symposium on Functional Analysis, Tokyo, 21–30. University of Tokyo Press.

Brown, L. G., R. G. Douglas, and P. A. Fillmore. 1977. “Extensions of C*-Algebras and K-Homology.” Annals of Mathematics 105 (2): 265–324. doi:10.2307/1970999.

Kasparov, G.G. 1975. “Topological Invariants of Elliptic Operators I: K-Homology.” Mathematics of the USSR — Izvestija 9: 751–92.