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Shape Fluctuations of Growing Droplets and Random Matrix Theory

Herbert Spohn
Technical University, Munich
March 18, 2011

We explain an exact solution of the one-dimensional Kardar-Parisi-Zhang equation with sharp wedge initial data. Physically this solution describes the shape fluctuations of a thin film droplet formed by the stable phase expanding into the unstable phase. In the long time limit our solution converges to the Tracy-Widom distribution of the largest eigenvalue of GUE random matrices.

p-Adic Analytic Continuation of Genus 2 Overconvergent Hilbert Eigenforms in the Inert Case

Yichao Tian
Princeton University; Member, School of Mathematics
March 17, 2011

A well known result of Coleman says that p-adic overconvergent (ellitpic) eigenforms of small slope are actually classical modular forms. Now consider an overconvergent p-adic Hilbert eigenform F for a totally real field L. When p is totally split in L, Sasaki has proved a similar result on the classicality of F. In this talk, I will explain how to treat the case when L is a quadratic real field and p is inert in L.