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Prof. Dennis Gaitsgory

Harvard University

“The Tamagawa number formula over function fields”

Friday, February 17, 2017 at 5 pm

203 Mathematics Hall

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.


The meeting is centered around recent advances in Schramm-Loewner Evolutions, Gaussian Free Field and Liouville Quantum Gravity.It will be held at Columbia University, March 13 – 17, 2017
Organizers: Julien Dubedat (Columbia), Fredrik Viklund (KTH).
The workshop is supported by the National Science Foundation (DMS 1308476)

For more information please visit: SLE, GFF AND LQG in NYC


 Thera Stochastics: A Mathematics Conference in Honor of Ioannis Karatzas

A conference to celebrate the contributions of Prof. Ioannis Karatzas will be held at The Petros M. Nomikos Conference Centre, Fira, Santorini, Greece.
Dates: May 31 – June 2, 2017
Organizers: Michail Anthropelos, Constantinos Kardaras, Marcel Nutz, Johannes Ruf

For more information, please visit the conference website:
Registration is required.

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