Analysis Seminar

Date:
Jan
31
2018

Analysis Seminar

Concentration inequalities for linear cocycles and their applications to problems in dynamics and mathematical physics
2:00pm|S-101

Given a measure preserving dynamical system, a real-valued observable determines a random process (by composing the observable with the iterates of the transformation). An important topic in ergodic theory is the study of the statistical properties...

Dec
06
2017

Analysis Seminar

Spectral gaps without frustration
Marius Lemm
2:00pm|S-101

In spin systems, the existence of a spectral gap has far-reaching consequences. So-called "frustration-free" spin systems form a subclass that is special enough to make the spectral gap problem amenable and, at the same time, broad enough to include...

Nov
29
2017

Analysis Seminar

Nonuniqueness of weak solutions to the Navier-Stokes equation
Tristan Buckmaster
2:00pm|S-101

For initial datum of finite kinetic energy Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this talk, I will discuss very recent joint work with Vlad Vicol in...

Nov
15
2017

Analysis Seminar

Thin monodromy and Lyapunov exponents, via Hodge theory
11:00am|S-101

I will discuss a connection between monodromy groups of variations of Hodge structure and the global behavior of the associated period map. The large-scale information in the period map is contained in the Lyapunov exponents, which are invariants...

Nov
08
2017

Analysis Seminar

Time quasi-periodic gravity water waves in finite depth
Massimiliano Berti
2:30pm|West Building Lecture Hall

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water waves solutions, namely periodic and even in the space variable $x$, of a bi-dimensional ocean with finite depth under the...

Nov
02
2017

Analysis Seminar

Two-bubble dynamics for the equivariant wave maps equation
Jacek Jendrej
11:00am|S-101

I will consider the energy-critical wave maps equation with values in the sphere in the equivariant case, that is for symmetric initial data. It is known that if the initial data has small energy, then the corresponding solution scatters. Moreover...

Nov
01
2017

Analysis Seminar

Structure theorems for intertwining wave operators
2:00pm|S-101

We will describe an implementation of the Wiener theorem in $L^1$ type convolution algebras in the setting of spectral theory. In joint work with Marius Beceanu we obtained a structure theorem for the wave operators by this method.

Oct
26
2017

Analysis Seminar

Quasi-periodic solutions to nonlinear PDE's
11:00am|S-101

We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE's. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a...

Oct
25
2017

Analysis Seminar

Nematic liquid crystal phase in a system of interacting dimers
2:00pm|S-101

In 1979, O. Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order...