Title: A two-dimensional analog of the Atiyah-Bott theorem
Speaker: Vladimir Kotov
Speaker Info: Northwestern University
Following Dennis Gaitsgory, we give a conceptual proof of a classical result of Atiyah and Bott about the cohomology ring of a moduli space Bun_G of G-principal bundles on an algebraic curve. We write down its cohomology as a chiral homology of a certain very natural chiral algebra on the curve. And then compute this chiral homology using various methods developed by Gaitsgory, Beilinson and Drinfeld.Date: Tuesday, November 27, 2012
We give an analog of this result for the two-dimensional case, where we use a Hilbert scheme of a surface in place of Bun_G. That is, we compute the cohomology of the Hilbert scheme in a very similar manner as we did for curves. We notice that the Hilbert scheme factorizes similarly to Beilinson-Drinfeld Grassmanian. Using this factorization structure, we find a chiral algebra on our surface, whose chiral homology is the cohomology ring of the Hilbert scheme.