# Upcoming Seminars & Events

## Primary tabs

##### Formation of Trapped Surfaces in General Relativity

An interesting question in general relativity is the dynamical formation of black holes for Einstein vacuum equation. In this talk, we will show that a trapped surface can dynamically form from arbitrary dispersed initial data in vacuum.

##### Some recent results on the Euler-Poincare model

Euler-Poincare equation was introduced by Holm, Marsden and Ratiu. It can be viewed as a natural multi-dimensional generalization of the popular Camassa-Holm equations. I will discuss some recent results on this model.

##### Homological stability of configurations spaces

Church [Homological stability for configuration spaces of manifolds, Invent. Math. 188 (2012),465--504] used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability.A second proof was also given by Randal-Williams [Homological stability for unordered configuration spaces, Q. J. Math.

##### TBA - Boxer

##### The structure of almost linear Boolean functions

A Boolean function f: {0,1}^n -> {0,1} is "linear" if it is a linear combination of its inputs. It is a simple exercise to show that a linear Boolean function depends on at most one coordinate. Friedgut, Kalai and Naor showed that if f is "almost" linear then it is "close" to a function depending on at most one coordinate.

##### Elliptic Curves and Knot Homology

Given a smooth elliptic curve E over the complex numbers we construct a functor-valued invariant of tangles, extending a known braid group action on the derived category of coherent sheaves on E^n. The invariant associated to a closed link L is related to odd Khovanov homology, and can be described in terms of the double cover branched over L.

##### On active scalar equations with nonlocal velocity.

The problem of finite-time singularity versus global regularity for active scalar equations with nonlocal velocities has attracted much attention in recent years. In this talk, I will discuss some recent results in this direction.

##### Structure of measures in Lipschitz differentiability spaces

This talk will present results showing the equivalence of two very different ways of generalising Rademacher's theorem to metric measure spaces. The first was introduced by Cheeger and is based upon

##### Inversion of adjunction for rational and Du Bois singularities

**Please note special day, time and location. ** This is joint work with Karl Schwede. We prove that Du Bois singularities are invariant under small deformation and that the relationship of the notions of rational and Du Bois singularities resembles that of canonical and log canonical varieties.

##### The pointwise convergence of Fourier Series near $L^1$

In this talk we discuss some recent developments on the old question regarding the pointwise behavior of Fourier Series near $L^1$. We start with several brief historical remarks on the subject, describing the context and the formulation of the main problem(s).

##### Coarsening to Chaos-Stabilized Fronts in Pattern Formation with Galilean Invariance

The presence of continuous symmetries, or coupling with a large-scale mode or mean flow, can strongly influence the dynamics of pattern-forming systems. After reviewing some aspects of pattern formation and spatiotemporal chaos in one-dimensional Kuramoto-Sivashinsky-type equations, I will focus on a 6th-order analogue, the Nikolaevskiy PDE, a model for short-wave pattern formation with Galile

##### Special Probability Seminar: Cover times, blanket times, and the Gaussian free field

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. The cover time of a finite graph G (the expected time for simple random walk to visit all vertices) has been extensively studied, yet a number of fundamental questions concerning cover times have remained open: Aldous and Fill (1994) asked whether there is a deterministic polynomial-time algorithm that computes the cover time up to an O(1) factor

##### Talk #2: TBA - Kleiner

##### Solving Boltzmann Equation, Green's Function Approach.

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. We will describe an quantitative approach for solving the Boltzmann equation in the kinetic theory. The approach has been developed, with Shih-Hsien Yu, in the past decade and proven effective in understanding some of the important physical phenomena.

##### On the Analogs of Szego Theorem for Ergodic Operators

We consider an asymptotic setting for ergodic operators generalizing that for the Szego theorem on the asymptotics of determinants of finite-dimensional restrictions of the Toeplitz operators. The setting is formulated via a triple consisting of an ergodic operator and two functions, the symbol and the test function.

##### TBA - Sarkar

##### 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.

##### Surface groups, representation spaces and rigidity

Let S_g denote the closed, genus g surface. In this talk, we'll discuss the space of flat circle bundles over S_g, also known as the "representation space" Hom(pi_1(S_g), Homeo+(S^1)). The Milnor-Wood inequality gives a lower bound on the number of components of this space (4g-3), but until very recently it was not known whether this bound was sharp.

##### 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.