Columbia University Mathematics Colloquium

C A N C E L L E D THIS WEEK February 11 Meets in room 312 this week Only.	C A N C E L L E D THIS WEEK Andrew J. Majda - Courant Institute	C A N C E L L E D THIS WEEK Information theory and predictability
February 18	Joyce McLaughlin - Rensselaer Polytechnic Institute	Interior elastodynamics inverse problems: Creating images of shear wave speed in human tissue Abstract: We extend the doctor's palpation exam, where he/she presses against the skin to feel a lump of abnormal tissue which is stiffer than normal tissue. Interior measurements of propagating shear waves are made with ultrasound. An inverse problem is solved with this data set to create the images. Well posedness results, unique continuation results, algorithms and images will be presented.
February 25 Meets in room 207 this week Only.	Albert Shiryaev - Moscow State University and Steklov Mathematics Institute	Mathematics of A.N.Kolmogorov Abstract: The talk centers on ideas of A.N.Kolmogorov in different areas of Mathematics
March 3	Winfried Kohnen - Universität Heidelberg	Special values of the $j$-function Abstract: Probably the simplest modular function of weight zero is the classical $j$-invariant in the theory of elliptic curves. The $j$ function classically is very important since for example its values at complex multicplication points are algebraic integers with interesting properties. The purpose of this talk is to give some recent results on the special values of $j$ at points in the divisor of an arbitrary non-zero modular form.
March 24	Oleg Viro - Uppsala Universitet	Patchworking in algebraic geometry and tropical geometry Abstract: Shortly tropical geometry can be described as an algebraic geometry over a semifield of real numbers with operations of maximum and addition. This is a piecewise linear geometry based on piecewise linear convex functions. It is incorporated in many ways into algebraic geometry over any other field, but the cases of real and complex fields are better understood. Real and complex algebraic varieties can be constructed via perturbation (or quantization) of tropical varieties. This construction is called combinatorial patchworking. It was invented by the speaker more than twenty years ago for constructing real algebraic curves with interesting topology.
April 7	Klaus Ecker - Freie Universität- Berlin	Mean curvature evolution of noncompact spacelike hypersurfaces
April 14 Joint Colloquium with Applied Mathematics	Jalal Shatah - Courant Institute	Schrodinger maps
April 21	Michael Harris - Université Paris VII & Columbia	Survey of p-adic representations of p-adic groups
April 28	Tetsuji Shioda - Rikkyo University	Integral points, abc and elliptic surfaces