**Title:** A two-dimensional analog of the Atiyah-Bott theorem

**Speaker:** Vladimir Kotov

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

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.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.

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