Analysis Seminar

Gamow introduced the liquid drop model in 1928 as a model for the nucleus. I will discuss some recent work (with Ian Ruohoniemi) concerning roundness of minimizers. 

Extremal black holes are special solutions of Einstein’s equations which have absolute zero temperature in the thermodynamic analogy of black hole mechanics. In this talk, I will present a proof that extremal black holes arise on the critical...

We consider an energy model for N ordered elastic membranes subject to forcing and boundary conditions. The heights of the membranes are described by real functions u_1, u_2,...,u_N, which minimize an energy functional involving the Dirichlet...

We study multiply warped product geometries MN:=Bn×Fn1×···×FnA 

g = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an open set of initial data within multiply warped product geometries the Ricci flow starting at any of those develops...

Hilbert’s sixth problem asks for a mathematically rigorous justification of the macroscopic laws of statistical physics from the microscopic laws of dynamics. The classical setting of this problem is the justification of Boltzmann’s kinetic equation...

I will present joint work with Jacek Jendrej. We consider classical scalar fields in dimension 1+1 with a symmetric double-well self-interaction potential. Examples of such equations are the phi-4 model and the sine-Gordon equation. These nonlinear...

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.

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...

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...

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...