Analysis Seminar

Consider a point particle flying freely on the torus and elastically bouncing back from the boundary of fixed smooth convex obstacles. This is the celebrated Sinai billiard, a rare example of a deterministic dynamical system where rigorous results...

In this talk, we will discuss some joint work with Alexandru Ionescu on the nonlinear inviscid damping near point vortex and monotone shear flows in a finite channel. We will put these results in the context of long time behavior of 2d Euler...

The study of hyperkaehler manifolds of lowest dimension (and of gauge theory on them) leads to a chain of generalizations of the notion of a quiver: quivers, bows, slings, and monowalls. This talk focuses on bows, their representations, and...

We consider a system of $N$ particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow, and possible added random diffusion. By Riesz interaction, we mean inverse power $s$ of the distance...

Given a polynomial $P$ of constant degree in $d$ variables and consider the oscillatory integral \[I_P = \int_{[0,1]^d} e(P(\xi)) \, \mathrm{d}\xi.\] Assuming the number $d$ of variables is also fixed, what is a good upper bound of $|I_P|$? In this...

In 2017 Lucio Galeati understood that a suitable scaling limit of certain hyperbolic PDEs with noise may lead to deterministic parabolic equations. Since then, in collaboration with Lucio and Dejun Luo, we have understood the phenomenon from several...

I will survey results related to graph comparison; graph comparison is a certain type of restriction on a metric spaces which is encoded by a given graph.

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...