Analysis Seminar

Date:
Feb
22
2021

Analysis Seminar

Spread of infections in random walkers
Allan Sly
4:30pm|Remote Access

We consider a class of interacting particle systems with two types, A and B which perform independent random walks at different speeds. Type A particles turn into type B when they meet another type B particle. This class of systems includes models...

Feb
08
2021

Analysis Seminar

Planarity in Higher Codimension Mean Curvature Flow
Keaton Naff
4:30pm|Remote Access

We will discuss the mean curvature flow of $n$-dimensional submanifolds in $\mathbb{R}^{n+k}$ satisfying a pinching condition $|A|^2 c|H|^2$ introduced by Andrews and Baker (2010). For suitable constants $c$, these flows resemble flows of convex...

Feb
01
2021

Analysis Seminar

Index theorems for nodal count and a lateral variation principle
Gregory Berkolaiko
4:30pm|Remote Access

Our study is motivated by earlier results about nodal count of Laplacian eigenfunctions on manifolds and graphs that share the same flavor: a normalized nodal count is equal to the Morse index of a certain energy functional at the critical point...

Jan
25
2021

Analysis Seminar

Bogoliubov theory for trapped Bose-Einstein condensates
4:30pm|Remote Access

We consider systems of $N$ particles interacting through a repulsive potential in the Gross-Pitaevskii regime. We prove complete Bose-Einstein condensation and we determine the form of the low-energy spectrum, in the limit of large $N$. Our results...

Jan
11
2021

Analysis Seminar

The ground state energy of dilute Bose gases
4:30pm|Simonyi 101 and Remote Access

The rigorous calculation of the ground state energy of dilute Bose gases has been a challenging problem since the 1950s. In particular, it is of interest to understand the extent to which the Bogoliubov pairing theory correctly describes the ground...

Dec
14
2020

Analysis Seminar

The singular set in the Stefan problem
Joaquim Serra
4:30pm|Remote Access

The Stefan problem, dating back to the XIX century, aims to describe the evolution of a solid-liquid interface, typically a block of ice melting in water. A celebrated work of Luis Caffarelli from the 1970's established that the ice-water interface...

Dec
07
2020

Analysis Seminar

Stability of discontinuous solutions for inviscid compressible flows
Alexis Vasseur
4:30pm|Remote Access

We will discuss recent developments of the theory of a-contraction with shifts to study the stability of discontinuous solutions of systems of equations modeling inviscid compressible flows, like the compressible Euler equation.

Nov
30
2020

Analysis Seminar

Sharp nonuniqueness for the Navier-Stokes equations
Xiaoyutao Luo
4:30pm|Remote Access

For the incompressible Navier-Stokes equations, classical results state that weak solutions are unique in the so-called Ladyzhenskaya-Prodi-Serrin regime. A scaling analysis suggests that classical uniqueness results are sharp, but current...