Ajay Ramadoss

Visiting Assistant Professor of Mathematics

Web Site N/A Contact Information Office:  580 Malott Hall Phone:  (607) 255-6400 Fax:  (607) 255-7149 Email:  ajaycr@math.cornell.edu Courses & Office Hours

Education

Ph.D. (2005) University of Chicago

Research Area: Algebraic geometry, noncommutative geometry, and homological algebra

Currently, my work is centered on Hochschild homology and its relation to some very familiar algebraic geometric theorems and constructions.

One direction I have pursued has involved the detailed study of the Mukai pairing (due to A. Caldararu) on the Hochschild homology of a smooth scheme. This has led to a higher analog of the Hirzebruch Riemann-Roch theorem. I hope to obtain other generalizations of the Hirzebruch Riemann-Roch theorem in the near future.

I have also worked on the construction of the integral over a complex manifold via “topological quantum mechanics” (originally due to B. Feigin, A. Losev and B. Shoikhet). This has led to an explicit link between the Hirzebruch Riemann-Roch and an algebraic Riemann-Roch theorem due to R. Nest and B. Tsygan. I hope to develop the methods I have used so far to understand other index theorems.

Selected Publications

The big Chern classes and the Chern character, International journal of Mathematics 19 no. 6 (2008), 699–746.

Some notes on the Feigin-Losev-Shoikhet integral conjecture, Journal of Noncommutative Geometry (to appear).

Integration over complex manifolds via Hochschild homology, Journal of Noncommutative Geometry (to appear).

The Mukai pairing and integral transforms in Hochschild homology (preprint).

Last modified: August 19, 2008