Upcoming Seminars & Events

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November 3, 2014
3:15pm - 4:30pm
Decouplings and applications

We describe a new Fourier analytic method for estimating a wide variety of exponential sums. The talk will mainly focus on  the applications to number theory and PDEs. This is joint work  with Jean Bourgain. 

Speaker: Ciprian Demeter , Indiana University
Location:
Fine Hall 314
November 3, 2014
4:30pm - 5:30pm
Set Oriented Numerical Methods for Dynamical Systems and Optimization

Over the last two decades so-called set oriented numerical methods have been developed in the context of the numerical treatment of dynamical systems. The basic idea is to cover the objects of interest - for instance invariant sets or invariant measures - by outer approximations which are created via multilevel subdivision techniques. At the beginning of this century these methods have been modified in such a way that they are also applicable to the numerical treatment of multiobjective optimization problems. Due to the fact that they are set oriented in nature these techniques allow for the direct computation of the entire so-called Pareto set.  In this talk recent developments in the area of set oriented numerics will be presented both for dynamical systems and optimization problems. The reliability of these methods will be demonstrated by several applications such as the approximation of transport processes in ocean dynamics, or the optimization of a cruise control with respect to energy consumption and travel distance. Moreover a new algorithmic idea will be described which allows to compute invariant sets directly by Newton's method.

Speaker: Michael Dellnitz , University of Paderborn, Germany
Location:
Fine Hall 214
November 5, 2014
2:00pm - 3:00pm
Fluctuations of the stationary Kardar-Parisi-Zhang equations

Up to a random height shift, two-sided Brownian motion is invariant for the Kardar-Parisi-Zhang equation. In this talk we describe recent results with Borodin, Ferrari and Veto through which we use Macdonald processes and the geometric Robinson-Schensted-Knuth correspondence to compute the distribution of this height shift and demonstrate cube-root fluctuations in large time, with a universal limit law. This also relates to the two-point correlation function and super-diffusivity of the stochastic Burgers equation.-

Speaker: Ivan Corwin, Clay Research Institute, Columbia University, Institut Henri Poincare
Location:
Fine Hall 322
November 6, 2014
3:00pm - 4:00pm
TBA - Holm
Speaker: Tara Holm , Cornell and the IAS
Location:
Fine Hall 314
November 6, 2014
3:00pm - 4:00pm
Few distinct distances and perpendicular bisectors

Let d(n) be the smallest number of distinct distances determined by any set of n points in the real plane. For n sufficiently large, is each set of n points that determines d(n) distances the intersection of an equalateral triangular lattice with a convex set? Is there at least a line that contains n^ε points, for some ε>0? Erdős asked these questions 30 years ago, and an argument due to Szemerédi shows that, if P is a set of points that determines n/k distances, then the perpendicular bisector of some pair of the points must be incident to k of the points. I will present an upper bound on the number of quadruples (x,y,z,w) among a set of points such that the perpendicular bisector of (x,y) is the same as the bisector of (z,w). Combined with Szemerédi's argument, this bound implies that set of n points that determines n/k distinct distances either includes Omega(n^{7/5}) collinear k-tuples, or a single circle or line contains Omega(n^{1/12}) points. Joint work with Adam Sheffer and Frank de Zeeuw.

Speaker: Ben Lund , Rutgers University
Location:
Fine Hall 224
November 6, 2014
4:30pm - 6:00pm
Thin knotted vortex tubes in stationary solutions to the Euler equation

In this talk we will discuss the proof of the existence of thin vortex tubes for stationary solutions to the incompressible Euler equation in R^3. More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in R^3, we will show that they can be transformed using a small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity.

 

Speaker: Alberto Enciso, ICMAT - Madrid
Location:
Fine Hall 322
November 6, 2014
4:30pm - 5:30pm
All finitely generated Kleinian groups of small Hausdorff dimension are classical Schottky groups

By the inspirational works of Peter Sarnak and Ralph Phillips (ACTA 1985), we know that all classical Schottky groups (dim n >3) must have Hausdorff dimension strictly bounded away from dim n-1. Later Peter Doyle (ACTA 1988) showed that it is also true for n=3. But the natural question of nonclassical Schottky groups should have Hausdorff dimension strictly bounded from below away from 0 remains open. In this second part of our works on geometric structure of Kleinian groups of small Hausdorff dimensions we provide positive solution to this question. In particular we prove that there exists a universal positive number $\lambda>0$, such that any finitely-generated non-elementary Kleinian groups with limit set of Hausdorff dimension $<\lambda$ are classical Schottky groups. We will base on our previous works done in (Geometry&Topology 2010 and JDG 2000) to prove our general result in this paper. We will discuss some applications and related questions.

Speaker: Yong Hou, Zanty Electronics
Location:
Fine Hall 314
November 6, 2014
4:30pm - 5:30pm
Representations of finite groups and applications

In the first part of the talk we will survey some recent results on representations of finite (simple) groups. In the second part we will discuss applications of these results to various problems in number theory and algebraic geometry.

Speaker: Pham Tiep , Harvard University / University of Arizona
Location:
IAS Room S-101
November 6, 2014
4:30pm - 6:00pm
TBA - Roquejoffre
Speaker: Jean-Michel Roquejoffre, University of Toulouse
Location:
Fine Hall 322
November 7, 2014
1:30pm - 2:30pm
TBA - Müller
Speaker: Stefan Müller , UIUC
Location:
IAS Room S-101
November 7, 2014
3:00pm - 4:00pm
TBA - Lee
Speaker: John Lee, University of Washington, Seattle
Location:
Fine Hall 314
November 7, 2014
4:15pm - 5:15pm
TBA - Chodosh
Speaker: Ottis Chodosh, Stanford University
Location:
Fine Hall 314
November 10, 2014
3:15pm - 4:30pm
TBA - Nahmod
Speaker: Andrea Nahmod, University of Massachusetts Amherst
Location:
Fine Hall 314
November 10, 2014
4:30pm - 5:30pm
The physical and mathematical structure of images

Images are both maps of continuous physical phenomena and discrete mathematical objects. While Shannon established the fundamental relationship between physical and mathematical images over half a century ago, considerable further progress in understanding this relationship has been achieved in the past quarter century through the development of wavelets and compressive measurement. This talk reviews simple physical models for the physical to mathematical transformation and discusses strategies for coding the physical interface to increase measurement efficiency. We specifically discuss novel sampling strategies for x-ray tomography, diffraction tomography and focal imaging. 

Speaker: David Brady , Duke University - Electrical & Computer Engineering
Location:
Fine Hall 214
November 11, 2014
4:30pm - 5:50pm
The structure of flow in Hydrodynamics, Thermodynamics and General Relativity, from Navier Stokes to Tolman

Problems with the formulation of Relativistic Astrophysics lead to the need for a variational formulation of thermodynamics. This is easy and immensely rewarding in the non relativistic context, so long as the motion is irrotational. The main topic of this talk is to overcome this limitation. The solution is amazingly simple; one has to combine two familiar forms of hydrodynamics. but it is shocking and even revolutionary nevertheless. Some basic tenets have to be given up, with interesting consequences. The application to General Relativity will be sketched at the end.

Speaker: Christian Fronsdal, UCLA
Location:
Jadwin Hall 343
November 12, 2014
2:00pm - 3:00pm
Infinite Dimensional Stochastic Differential Equations for Dyson's Brownian Motion

Dyson's Brownian Motion (DBM) describes the evolution of the spectra of certain random matrices, and is governed by a system of stochastic differential equations (SDEs) with a singular, long-range interaction. In this talk I will outline a construction of the strong solution of the infinite dimensional SDE that corresponds to the bulk limit of DBM. This is a pathwise construction that allows an explicit space with generic configurations. The ideas used further lead to a proof of the pathwise uniqueness of the solution and of the convergence of the finite to infinite dimensional SDE.

Speaker: Li-Cheng Tsai, Stanford University
Location:
Fine Hall 322
November 13, 2014
2:00pm - 3:30pm
TBA - Hooper
Speaker: Pat Hooper , City College of New York, City University of New York
Location:
Fine Hall 601
November 13, 2014
3:00pm - 4:00pm
Saturation in the hypercube

A subgraph of the d-dimensional cube Qd is (Qd,Qm)-saturated if it does not contain a copy of Qm, but adding any missing edge creates a copy of Qm. The subgraph is weakly (Qd,Qm)-saturated if we can add the missing edges one at a time, creating a new copy of Qm at each step. Answering a question of Johnson and Pinto, we show that for every fixed m, the minimum number of edges in a (Qd,Qm)-saturated graph is \Theta(2^d). We also determine exactly the minimum number of edges in a weakly (Qd,Qm)-saturated subgraph of Qd, and raise some further questions. Joint work with Natasha Morrison and Jonathan Noel.

Speaker: Alex Scott , Oxford University
Location:
Fine Hall 224
November 13, 2014
4:30pm - 5:30pm
3-manifolds, Lipschitz geometry, and equisingularity

The local topology of isolated complex surface singularites is long understood, as cones on closed 3-manifolds obtained by negative definite plumbing. On the other hand a full understanding of the analytic types is out of reach, motivating Zariski's efforts into the 1980's to give a good concept of "equisingularity" for families of singularities. The significance of Lipschitz geometry as a tool in singularity theory is a recent insight, starting (in complex dimension 2) with examples of Birbrair and Fernandes published in 2008. I will describe work with Birbrair and Pichon on classifying this geometry in terms of discrete data associated with a refined JSJ decomposition of the associated 3-manifold link. Also work with Anne Pichon proving that Zariski equisingularity in this dimension (and lower) is equivalent to constant Lipschitz geometry.

Speaker: Walter Neumann , Columbia University
Location:
Fine Hall 314
November 13, 2014
4:30pm - 6:00pm
TBA - Germain
Speaker: Pierre Germain , NYU
Location:
Fine Hall 322

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