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 NN 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 ss of the distance...

Given a polynomial PP of constant degree in dd variables and consider the oscillatory integral

IP=?[0,1]de(P(?))d?.IP=?[0,1]de(P(?))d?.

Assuming the number dd of variables is also fixed, what is a good upper bound of |IP||IP|? In this talk, I...

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.

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 nn-dimensional submanifolds in ?n+kRn+k satisfying a pinching condition |A|2

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...

We consider systems of NN 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 NN. Our results...