Analysis Seminar

Date:
Dec
01
2023

Joint IAS/PU Analysis Seminar

Renormalization Group and Homogenization
Scott Armstrong
4:00pm|Simonyi 101 and Remote Access

I will describe some new "coarse-graining" methods in quantitative homogenization and how they can be used to give rigorous versions of certain heuristic "renormalization group" arguments in physics, with a focus on several examples.

Dec
01
2023

Joint IAS/PU Analysis Seminar

Higher Dimensional Fractal Uncertainty
Alex Cohen
2:30pm|Simonyi 101 and Remote Access

A fractal uncertainty principle (FUP) roughly says that a 
function and its Fourier transform cannot both be concentrated on a 
fractal set. These were introduced to harmonic analysis in order to 
prove new results in quantum chaos: if eigenfunctions...

Oct
13
2023

Joint IAS/PU Analysis Seminar

Immortal Solutions of the Kähler-Ricci Flow
Valentino Tosatti
4:00pm|Princeton University, Fine Hall 314

I will discuss the problem of understanding the long-time behavior of Ricci flow on a compact Kähler manifold, assuming that a solution exists for all positive time. Inspired by an analogy with the minimal model program in algebraic geometry, Song...

Oct
13
2023

Joint IAS/PU Analysis Seminar

On the Long-Time Behavior of Solutions to the 2d Euler Equation
Tarek Elgindi
2:30pm|Princeton University, Fine Hall 314

We will describe a recent result on the stability of twisting in 2d Hamiltonian flows and its application to various questions concerning the long-time behavior of 2d Euler solutions. We will look at stability properties of stationary solutions...

Jun
14
2021

Analysis Seminar

Local Dissipation of Energy for Continuous Incompressible Euler Flows
Phillip Isett
4:30pm|Remote Access

I will discuss the construction of continuous solutions to the incompressible Euler equations that exhibit local dissipation of energy and the surrounding motivations. A significant open question, which represents a strong form of the Onsager...

Jun
07
2021

Analysis Seminar

Geodesics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Reeb flow
Yves Colin de Verdière
4:30pm|Remote Access

Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat (Paris). A 3D closed manifold with a contact distribution and a metric on it carries a canonical contact form. The associated Reeb flow plays a central role for the asymptotics of the...

May
24
2021

Analysis Seminar

The Schrodinger equations as inspiration of beautiful mathematics
Gigliola Staffilani
4:30pm|Remote Access

In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of...

May
17
2021

Analysis Seminar

Eigenfunction concentration via geodesic beams
Yaiza Canzani
4:30pm|Remote Access

A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction...