Analysis Seminar

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

IP=∫[0,1]de(P(ξ))dξ.IP=∫[0,1]de(P(ξ))dξ.

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

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 ℝn+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...

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...

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...