# Seminars & Events for 2013-2014

##### Geometric Structure And The Local Langlands Conjecture

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. Let G be a connected split reductive p-adic group. Examples are GL(n,F ), SL(n, F ), SO(n, F ), Sp(2n, F ), PGL(n, F ) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers.

##### The Green-Tao Theorem and a Relative Szemerédi Theorem

The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. In this talk, I will explain the ideas of the proof and recent joint work with David Conlon and Yufei Zhao simplifying the proof.

##### Recovering elliptic curves from their p-torsion

**Please note special day (Friday) and time (11:00 a.m.) **Given an elliptic curve E over a field k, its p-torsion E[p] gives a 2-dimensional representation of the Galois group G_k over F_p. The Frey-Mazur conjecture asserts that for k=Q and p>13, E is in fact determined up to isogeny by the representation E[p]. In joint work with J.

##### Asymptotics of minimal submanifolds in AdS/CFT correspondence

The talk will describe the asymptotics of minimal submanifolds in spaces which are the product of an asymptotically hyperbolic manifold and a compact Riemannian manifold. Such spaces arise in the AdS/CFT correspondence in physics. Results include the derivation of a minimality constraint on the boundary submanifold and an identification of the local data necessary to determine the asymptotics

##### Rational curves in quiver varieties

We will first review the general structural features of quantum multiplication and then discuss the key points that allow to determine it for Nakajima varieties.

##### Global well-posedness of incompressible elastodynamics in 2D

I will report our recent result on the global wellposedness of classical solutions to system of incompressible elastodynamics in 2D. The system is revealed to be inherently strong linearly degenerate and

automatically satisfies a ***strong*** null condition, due to the isotropic nature and the incompressible constraint.

##### Graph limits and planted partitions from the perspective of probability and statistics

**SPECIAL PACM COLLOQUIUM: **The theory of dense graph limits has emerged as a well established tool in modern combinatorics, with close connections to applied probability and ergodic theory.

##### A new approach to derandomize compressed sensing matrices

The restricted isometry property (RIP) is a compressed sensing matrix specification which leads to performance guarantees for a wide variety of sparse signal reconstruction algorithms. For the sake of quality sensing standards, practitioners desire deterministic sensing matrices, but the best known deterministic RIP matrices are vastly inferior to those constructed using random processes.

##### A model theory for adeles and connections to number theory

This is joint work with Angus Macintyre. Using p-adic model theory and other tools, we develop a model theory for the adeles of a number field. I will state some of the main results, and discuss some recent emerging connections to Serre's work on the number of solutions modulo p of a variety, to analytic properties of zeta and L-functions, and to adelic Poisson summation formulas.

##### Long time behavior of the Navier-Stokes and related equations

I will review some resent results on the long time behavior of equations arising in fluid dynamics, such as the 3D Navier-Stokes and critical surface quasi-geostrophic equations.

##### Moments of zeta functions associated to hyperelliptic curves

I will discuss conjectures, theorems, and experiments concerning the moments, at the central point, of zeta functions associated to hyperelliptic curves over finite fields of odd characteristic. Let $q$ be an odd prime power, and $H_{d,q}$ denote the set of square-free monic polynomials $D(x) \in F_q[x]$ of degree $d$. Let $2g=d-1$ if $d$ is odd, and $2g=d-2$ if $d$ is even.

##### Outlook

I will explain how what we learned is applied in the enumerative geometry of curves in 3-folds and talk about various directions in which it can be generalized.

##### On CLT for Linear Statistics in Random Matrices

I will discuss recent CLT type results for linear eigenvalue statistics and related objects in various ensembles of Random Matrices. Joint works with Lingyun Li (UC Davis) and Sean O'Rourke (Yale).

##### Women and Mathematics

Each year the Princeton Mathematics Department and the Institute for Advanced Study co-sponsor a "Women and Mathematics" program. This year the day of the program at Fine Hall will be May 19th. Please click the title for the day's schedule.

##### From conformal invariance of parafermionic observables to conformal invariance of interfaces of planar random-cluster models

In this talk we will explain how the determination of the scaling limit of parafermionic observables can be used to deduce the conformal invariance of interfaces in planar random-cluster models with cluster-weight 1 ≤ Q ≤ 4 (1\leq Q \leq 4). The strategy was introduced in the context of the loop-erased random walk by Lawler-Schramm-Werner, and was implemented for the FK Ising model (a.k.a.

##### 2014 Alumni Reunion Open House

The Mathematics Department will hold our 2014 Alumni Open House on Friday, May 30th.Refreshments will be served and there will be short talks by faculty, graduate and undergraduate students.

##### Euler Systems and the Birch-Swinnerton-Dyer

**This is a Special Number Theory Seminar: **

##### Euler Systems and bounds for Selmer groups

**This is a Special Number Theory Seminar.**

##### 2014 International Workshop on Structure in Graphs and Matroids

The aim of this 5-day workshop is to bring together leading researchers in Graph Theory and Matroid Theory, to encourage communication and collaboration between these researchers, and to bring a new generation of researchers up to date with the exciting developments in the fields.