This is the home page for MATH 597A, Fall 2014, a “special topics” course for advanced graduate students.
Our objective for this course will be to study the following classic papers
- Atiyah, M. F., and R. Bott. “A Lefschetz Fixed Point Formula for Elliptic Complexes: I.” Annals of Mathematics 86, no. 2 (September 1, 1967): 374–407 and “A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications.” Annals of Mathematics 88, no. 3 (November 1, 1968): 451–91
- Atiyah, M. F., and I. M. Singer. “The Index of Elliptic Operators: I.” Annals of Mathematics, 87, no. 3 (May 1968): 484–530 and “The Index of Elliptic Operators: III.” Annals of Mathematics, 87, no. 3 (May 1968): 546–604.
- Atiyah, M.F., R. Bott, and V. K. Patodi. “On the Heat Equation and the Index Theorem.” Inventiones Mathematicae 19, no. 4 (December 1, 1973): 279–330.
- Atiyah, M.F., V.K. Patodi, and I.M. Singer. “Spectral Asymmetry and Riemannian Geometry I.” Mathematical Proceedings of the Cambridge Philosophical Society 77 (1975): 43–69.
That doesn’t mean that we are going to walk step by step through all these papers. I will jump about quite a bit and supply background information of various kinds. We will however continually refer back to these papers so you will need to get copies of all of them (you can download these from JSTOR). From time to time I may well ask class members to prepare presentations on some topics that arise in our discussoin.