# Seminars & Events for 2013-2014

##### Uniformity of harmonic map heat flow at infinite time

We will discuss an energy convexity along the harmonic map heat flow with small initial energy and fixed boundary data on the unit 2-disk. In particular, this shows that such weak harmonic map heat flow converges uniformly in time strongly in the W^{1,2}-topology, as time goes to infinity, to the unique limiting harmonic map.

##### Global regularity for 2d water waves

We consider the water waves system for the evolution of a perfect irrotational fluid with a free boundary, in 2 spatial dimensions, under the influence of gravity. We prove the existence of global solutions for suitably small and regular initial data. We also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear, unlike the 3 dimensional case.

##### TBA - Brown

##### H\"older estimates for fully nonlinear parabolic integro-differential equations

**Please note special day, time and location. **We will revisit H\"older estimates for some non local problems we worked recently with G. D\'avila. They arise in stochastic optimal control

##### Smooth Structures in Low-Dimensional Topology

Smooth 4-manifolds are without question the least understood topic in low-dimensional topology. In dimensions 5 and higher, the h-cobordism theorem handles most of the difficulties, while in dimensions 3 and below, smooth and topological manifolds coincide.

##### An infinite rank summand of topologically slice knots

Let C_{TS} be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that C_{TS} contains an infinite rank subgroup, and Livingston and Manolescu-Owens showed that C_{TS} contains a Z^3summand. We show that in fact C_{TS} contains a Z^\infty summand.

##### Complex analytic vanishing cycles for formal schemes

Let $R={\cal O}_{{\bf C},0}$ be the ring of power series convergent in a neighborhood of zero in the complex plane. Every scheme $\cal X$ of finite type over $R$ defines a complex analytic space ${\cal X}^h$ over an open disc $D$ of small radius with center at zero. PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT.

##### Recent progress in distinct distances problems

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. During 2013, significant progress has been made on several problems that are related to the Erdos distinct distances problem. In this talk I plan to briefly describe some of these results and the tools that they rely on. I will focus on the following two results.

##### Lagrangian submanifolds of complex projective space

First, I will discuss a proof that a Lagrangian torus in ℂℙ2 arising from a semitoric system described by Weiwei Wu coincides with the image in ℂℙ2 of Chekanov's exotic Lagrangian torus in ℝ4.

##### On the singularities of the Szego projections on CR manifolds

In this talk, I will report the first part of my paper(Projections in several complex variables, Mem. Soc. Math. France, 2010, 131 p.). In this work, we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold.

##### On base point freeness in positive characteristic

**Please note special day and time. **Many of the results in the Minimal Model Program depend on Kodaira vanishing theorem and its generalizations. On the other hand, because of the failure of these tools in positive characteristic, many of these results are still open in this case.

##### CANCELLED: Topological recursion in random matrices, random maps, and differential systems

**THIS SEMINAR HAS BEEN CANCELLED.**

##### Differential forms in Heisenberg groups and div-curl systems

In this talk we present a result proved in collaboration with Annalisa Baldi. We prove a family of inequalities for differential forms in Heisenberg groups (Rumin’s complex), that are the natural counterpart of a class of div-curl inequalities in de Rham’s complex proved by Lanzani & Stein, Bourgain & Brezis.

##### Intertwinings, wave equations and growth models

**Special Probability Seminar: **We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion.

##### The log zoo

The compact four-manifolds that admit a Kahler metric with positive Ricci curvature have been classified in the 19th century: they come in 10 families.

##### A remark on the Euler equations of hydrodynamics

**Please note special day and time. **The time evolution of an ideal incompressible fluid is described by the Euler equations. In this mostly speculative talk I will discuss a connection between stationary solutions of these equations and symplectic topology, as well as possible applications to questions of hydrodynamic instability.

##### Linear Stability of the Schwarzschild Solution under gravitational perturbations

I will talk about recent work joint with M. Dafermos and I. Rodnianski establishing the linear stability of the Schwarzschild solution. Key to the proof is a novel quantity which decouples from the system of gravitational perturbations and satisfies a wave equation, for which decay estimates can be proven. I will also connect the result to the non-linear stability problem.

##### Inferring and Encoding Graph Partitions

Connections among disparate approaches to graph partitioning may be made by reinterpreting the problem as a special case of one of either of two more general and well-studied problems in machine learning: inferring

##### On the volume of isolated singularities

Boucksom, de Fernex and Favre defined a non-log-canonical volume to study isolated singularities and developed several geometric results. Their definition is based on the intersection number of nef envelope of the log discrepancy b-divisor. In this talk, I will give an alternate definition of this volume by log canonical modification.

##### The triangulation conjecture

The triangulation conjecture stated that any n-dimensional topological manifold is homeomorphic to a simplicial complex. It is true in dimensions at most 3, but false in dimension 4 by the work of Casson and Freedman. In this talk I will explain the proof that the conjecture is also false in higher dimensions.