Seminars & Events for 2012-2013

November 12, 2012
3:15pm - 4:15pm
Scalar equations as asymptotic models for internal waves in Oceanography

We propose to derive rigorously scalar asymptotic models for the propagation of gravity waves at the interface between two layers of immiscible fluids of different densities (modeling fresh and salt water interface).

Speaker: Vincent Duchene , Columbia University
Location:
Fine Hall 314
November 12, 2012
4:30pm - 5:30pm
Robust Subspace Modeling

Consider a dataset of vector-valued observations that consists of a modest number of noisy inliers, which are explained well by a low-dimensional subspace, along with a large number of outliers, which have no linear structure. We describe a convex optimization problem that can reliably fit a low-dimensional model to this type of data. When the inliers are contained in a low-dimensional subspace we provide a rigorous theory that describes when this optimization can recover the subspace exactly. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

Speaker: Gilad Lerman, University of Minnesota
Location:
Fine Hall 214
November 13, 2012
2:00pm - 3:30pm
Traps and Random Walks in Random Environments on a Strip

PLEASE NOTE SPECIAL DAY (TUESDAY, NOV. 13)

Speaker: Ilya Goldsheid , Queen Mary College
Location:
Fine Hall 801
November 13, 2012
3:30pm - 5:00pm
Towards crystallization in Coulomb systems

We are interested in the statistical mechanics of (classical) two-dimensional Coulomb gases and one-dimensional log gases in a confining potential. We connect the Hamiltonian to the "renormalized energy", a way to compute the total Coulomb interaction of an infinite jellium, and whose minimum is expected to be achieved by the triangular lattice in 2D, and is achieved by the lattice Z in 1D.

Speaker: Sylvia Serfaty , (Université Pierre et Marie Curie - Paris 6 and Courant Institute)
Location:
Jadwin Hall A06
November 13, 2012
4:30pm - 6:00pm
MMP for moduli spaces of sheaves on K3 surfaces and Cone Conjectures

We report on joint work in progress with A. Bayer on how one can use wall-crossing techniques to study the birational geometry of a moduli space M of Gieseker-stable sheaves on a K3 surface X. In particular:
(--) We will give a "modular interpretation" for all minimal models of M.

Speaker: Emanuele Macrì , The Ohio State University
Location:
Fine Hall 322
November 15, 2012
12:30pm - 1:30pm
Open problems in mathematical general relativity

Introduced by Einstein in 1915, the theory of general relativity is probably one of the most well-tested theories in physics. And yet a basic mathematical understanding of this theory is lacking (for no other
reason than being difficult).  I would like to introduce some of the major open questions.

Speaker: Jonathan Kommemi, Princeton University
Location:
Fine Hall 314
November 15, 2012
2:00pm - 3:30pm
How long does it take to catch a drunk miscreant?

We discuss the answer to a question of Churchley who asked how long it will take a cop to catch a drunk robber who moves randomly. We begin by discussing other variants of the cop-robber paradigm. This is
joint work with Alex Scott, Colin McDiarmid, and Ross Kang. We rely heavily on work of Komarov and Winkler.

Speaker: Bruce Reed , McGill University
Location:
Fine Hall 224
November 15, 2012
2:00pm - 3:30pm
On Littlewood’s conjecture in Diophantine approximation

The purpose of my talk will be to present some of the results that have been established for Littlewood’s conjecture. In the first part of the discussion I will give an expository overview of what is currently known about the conjecture and what are some of the questions that naturally arise from it.

Speaker: Evgeni Dimitrov, Princeton University
Location:
Fine Hall 601
November 15, 2012
3:00pm - 4:00pm
Deformations of periodic frameworks

A d-periodic bar-and-joint framework is an abstraction (and generalization to arbitrary dimension d) of an atom-and-bond crystal structure. We describe a deformation theory for this type of frameworks

Speaker: Ciprian Borcea, Rider University
Location:
Fine Hall 214
November 15, 2012
4:30pm - 5:30pm
Galois representations for regular algebraic cuspidal automorphic forms

To any essentially self-dual, regular algebraic (ie cohomological) automorphic representation of GL(n) over a CM field one knows how to associate a compatible system of l-adic representations. These l-adic representations occur (perhaps slightly twisted) in the cohomology of a Shimura variety.

Speaker: Richard Taylor , IAS
Location:
IAS Room S-101
November 16, 2012
3:00pm - 4:00pm
On the degeneracy of optimal transport

It is a well known result of Caffarelli that an upper and lower bound on the Monge-Amp{\`e}re measure of a convex function u implies the function must actually be strictly convex.

Speaker: Jun Kitagawa, University of British Columbia
Location:
Fine Hall 314
November 16, 2012
4:30pm - 5:30pm
Abstract analogues of flux as symplectic invariants

This talk is part of a circle of ideas that one could call "categorical dynamics". We look at how objects of the Fukaya category move under deformations prescribed by fixing an odd degree quantum cohomology class. This is an analogue of moving Lagrangian submanifolds under non-Hamiltonian deformations.

Speaker: Paul Seidel, MIT
Location:
IAS - Simonyi Hall Seminar Room SH-101
November 19, 2012
3:15pm - 4:15pm
Global results for linear waves on expanding Schwarzschild de Sitter cosmologies

In this talk I will present recent results for solutions to the linear wave equation on Schwarzschild de Sitter black hole spacetimes. We focus here on the expanding region of the spacetime, and exhibit a stability mechanism which manifests itself in a global redshift effect. I shall describe how this can be combined with earlier results to obtain a global linear stability result.

Speaker: Volker Schlue , University of Toronto
Location:
Fine Hall 314
November 19, 2012
4:30pm - 5:30pm
How to Design Simple Efficient Mechanisms that are also Composable

SPECIAL JOINT SEMINAR WITH COMPUTER SCIENCE. E-commerce applications require simple, and well-designed systems, and systems that work well even if users participate in multiple mechanisms (and the value of each player overall is a complex function of their outcomes). Traditional mechanism design has considered such mechanisms only in isolation, and the mechanisms it proposes tend to be complex and impractical. In contrast, players typically participate in various mechanisms, mechanisms that are run by different principals (e.g. different sellers on eBay or different ad-exchange platforms) and coordinating them to run a single combined mechanism is infeasible or impractical. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

Speaker: Eva Tardos , Cornell University
Location:
105 Computer Science
November 20, 2012
4:30pm - 6:00pm
Rationality in families of threefolds

In a joint work with Tommaso de Fernex, we prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of separably rationally connected fibers.

Speaker: Davide Fusi, University of Utah
Location:
Fine Hall 322
November 26, 2012
3:15pm - 4:15pm
On a class of super-critical quasi-geostrophic type models in fluid dynamics

I will discuss some recent results on a class of active scalars with non-local transport and super-critical dissipation. Part of the talk is based on some joint work with Hongjie Dong.

Speaker: Dong Li , University of British Columbia / IAS
Location:
Fine Hall 314
November 26, 2012
4:30pm - 5:30pm
Dynamics of a Cytokine Storm

Six volunteers experienced severe inflammatory response during the Phase I clinical trial of a monoclonal antibody that was designed to stimulate a regulatory T cell response. Soon after the trial began, each volunteer experienced a "cytokine storm", a dramatic increase in cytokine concentrations. (CLICK ON SEMINAR TITLE FOR FULL ABSTRACT.)

Speaker: Robert Stengel, Princeton University
Location:
Fine Hall 214
November 27, 2012
4:30pm - 6:00pm
Enumeration of singular curves with tangency conditions

How many nodal degree d plane curves are tangent to a given line? The celebrated Caporaso-Harris recursion formula gives a complete answer for any number of nodes, degrees, and all possible tangency conditions.

Speaker: Yu-Jong Tzeng , Harvard University
Location:
Fine Hall 322
November 29, 2012
12:30pm - 1:30pm
On Fluid Mechanics and its Difficulties

I'll spend the first half (but hopefully less) of the talk giving an abridged introduction to the Euler and Navier-Stokes equations, covering the basic derivations and some of the known results. Afterwards, I will provide two examples to illustrate some of the difficulties in analyzing these equations.

Speaker: Andrei Tarfulea , Princeton University
Location:
Fine Hall 314
November 29, 2012
2:00pm - 3:30pm
A Szemeredi-Trotter theorem in R^4

The Szemeredi-Trotter theorem states that m points and n lines in the plane can have at most O(m^{2/3}n^{2/3}+m+n) incidences. This theorem has seen a number of generalizations, including a theorem of Toth that obtains the same result for (complex) points and lines in the complex plane. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

Speaker: Josh Zahli , UCLA
Location:
Fine Hall 224

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