## QUESTION SESSION ON GRASSMANNIANS, POLYTOPES AND QUANTUM FIELD THEORY

This is a continuation of Tuesday's talk.

Nima Arkani-Hamed

Professor, School of Natural Sciences

March 18, 2011

This is a continuation of Tuesday's talk.

Derek Bermel and Rossen Milanov

Institute for Advanced Study, Princeton Symphony Orchestra

March 18, 2011

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.

David Geraghty

Princeton University; Member, School of Mathematics

March 17, 2011

Richard Taylor

Harvard University; Distinguished Visiting Professor, School of Mathematics

March 17, 2011

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.

Wladimir de Azevedo Pribitkin

College of Staten Island, CUNY

March 17, 2011

Yiannis Sakellaridis

Member, School of Mathematics

March 16, 2011

Periods of automorphic forms over spherical subgroups tend to: (1) distinguish images of functorial lifts and (2) give information about L-functions.

This raises the following questions, given a spherical variety X=H\G: Locally, which irreducible representations admit a non-zero H-invariant functional or, equivalently, appear in the space of functions on X? Globally, can the period over H of an automorphic form on G be related to some L-value?

Igor Rivin

Temple University; Member, School of Mathematics

March 16, 2011

Daniel Kane

Harvard University

March 15, 2011

We define a polynomial threshold function to be a function of the form f(x) = sgn(p(x)) for p a polynomial. We discuss some recent techniques for dealing with polynomial threshold functions, particular when evaluated on random Gaussians. We show how to use these ideas to produce a pseudo random generator for degree-d polynomial threshold functions of Gaussians with seed length poly(2^d,log(n),epsilon^{-1}) .