Analysis Seminar

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...

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...

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...