Title: On the stability of black holes
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Title: Mirror maps for hypersurfaces and ordinary differential equations Print this pageThe spring 2017 Ritt Lectures, by Prof. William Minicozzi, will take place on Monday March 27 , and Tuesday, March 28. Prof. Minicozzi (Massachusetts Institute of Technology), will deliver a two talk series titled: “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 Tea will be served at 4 pm in 508 Mathematics
Print this pageTitle: Modularity of generating series of arithmetic divisors on unitary Shimura varieties Print this pageOn February 17 there will be a half-day symposium featuring a series of short talks by Columbia faculty working on probability and its interactions with society. Date: Friday, February 17th Schedule: 9:00am : Introduction — Ivan Corwin (Mathematics) A light pizza lunch will be provided afterwards in the Cantor Lounge, room 508 Mathematics. (This event is cohosted by members of the departments of Applied Physics & Applied Mathematics, Industrial Engineering & Operations Research, Mathematics, Statistics, Data Science Institute) Print this pageThe 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 Print this page |
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