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Spring 2017 Ellis R. Kolchin Lecture by Prof. Dennis Gaitsgory

The spring 2017 iteration of the Ellis R. Kolchin Memorial Lecture will be delivered by Prof. Dennis Gaitsgory (Harvard) on Friday, February 17th, 2017. Prof. Gaitsgory will give the following lecture:

“The Tamagawa number formula over function fields”

Let X be a curve over a finite field and let G be a semisimple algebraic group. The Tamagawa number formula can be interpreted as saying that the number of isomorphism classes of G-bundles on X (each counted with the multiplicity equal to 1/{order of the group of automorphisms}) equals the Euler product where each closed point x of X contributes 1/|G(k_x)|, where k_x is the residue field at x. We will deduce this equality from interpreting the cohomology of the moduli space Bun_G of G-bundles on X as a ‘continuous tensor product’  (technically, chiral homology) of copies of the cohomology of the classifying space BG of G along X. The latter identification of H^*(Bun_G) makes sense over an arbitrary ground field k, and when k is the field of complex numbers, it amounts to the Atiyah-Bott formula. We will give an algebro-geometric proof by first relating H^*(Bun_G) to the cohomology of the affine Grassmannian, and then performing a fancy version of Koszul/Verdier duality.   This is joint work with Jacob Lurie.

Friday, February 17, 2017 at 5 pm

203 Mathematics Hall

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