## 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.

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

Nima Arkani-Hamed
Professor, School of Natural Sciences
March 18, 2011

This is a continuation of Tuesday's talk.

## Niebur Integrals and Mock Automorphic Forms

College of Staten Island, CUNY
March 17, 2011

## Automorphy Theorems II

David Geraghty
Princeton University; Member, School of Mathematics
March 17, 2011

## Applications

Richard Taylor
Harvard University; Distinguished Visiting Professor, School of Mathematics
March 17, 2011

## 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.

## Periods Over Spherical Subgroups: An Extension of Some of the Langlands Conjectures

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?

## The (Unreasonable) Effectiveness of (Hyperbolic) Geometry

Igor Rivin
Temple University; Member, School of Mathematics
March 16, 2011

## A PRG for Gaussian Polynomial Threshold Functions

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}) .
{"ft_lang_label":"__label__en","ft_lang_prob":0.78405464,"math_prob":0.70154035,"size":446,"snap":"2019-26-2019-30","text_gpt3_token_len":89,"char_repetition_ratio":0.122171946,"word_repetition_ratio":0.0,"special_character_ratio":0.16143498,"punctuation_ratio":0.04109589,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95271915,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-23T20:05:27Z\",\"WARC-Record-ID\":\"<urn:uuid:df4df42a-a53e-4097-a376-409f9aff19c4>\",\"Content-Length\":\"31832\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f87f0224-b76f-4065-a3a3-1172911f27e5>\",\"WARC-Concurrent-To\":\"<urn:uuid:817b6602-cbf1-489a-9bc2-5215c0076a4e>\",\"WARC-IP-Address\":\"50.16.199.39\",\"WARC-Target-URI\":\"https://video.ias.edu/frontpage?amp%3Bamp%3Bs=earn-make-money.com/2011/09/how-to-make-money-on-ebay-discovering-nichelaunchinganebaybusinessiseasyfunandcanbedonefromthecomfortofthepersonalhomeguide&page=265\",\"WARC-Payload-Digest\":\"sha1:IYQAZKUQH47EUST6JKK4KTGO4FAPICQH\",\"WARC-Block-Digest\":\"sha1:N2XGJRQKPWOL63FLJPJXOERAFFIQF3TG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195529664.96_warc_CC-MAIN-20190723193455-20190723215455-00524.warc.gz\"}"}