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**JOSEPH FELS RITT LECTURES**

William Minicozzi (MIT)

“Level set method for motion by mean curvature”

Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to a degenerate elliptic nonlinear pde. A priori solutions are only defined in a weak sense, but it turns out that they are always twice differentiable classical solutions. This result is optimal; their second derivative is continuous only in very rigid situations that have a simple geometric interpretation. The proof weaves together analysis and geometry. This is joint work with Toby Colding.

Monday &Tuesday, March 27 & 28, 2017 at 4:30 pm

520 Mathematics Hall, 2990 Broadway at 117th Street

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**ELLIS R. KOLCHIN MEMORIAL LECTURE**

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.

**SLE, GFF and LQG in NYC**

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:

http://www.math.columbia.edu/department/thera/index.shtml

Registration is required.