Previous Special Year Seminar

In these two talks, I will discuss the structure of certain varieties that depend functorially on the choice of a finite-dimensional vector space. Examples include the variety of d-way tensors of "slice rank" at most k and the variety of degree-d...

Given a topological dynamical system $(X,T)$ a bounded sequence $(a_n)$ and $f\in C(X)$ we are interested in the asymptotic behavior of $$\frac{1}{\sum_{n\leq N}|a_n|}\sum_{n\leq N}a_nf(T^nx)$$

This will be a survey talk about recent progress on pointwise convergence problems for multiple ergodic averages along polynomial orbits and their relations with the Furstenberg-Bergelson-Leibman conjecture.

We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations.  Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby...

In this three-part lecture series, we will present a series of works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic mixing and enhanced dissipation properties of a passive tracer subject to the motion of an ergodic Markovian flow of...

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the...

In this three-part lecture series, we will present a series of works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic mixing and enhanced dissipation properties of a passive tracer subject to the motion of an ergodic Markovian flow of...

I will present a recent result jointly with Francisco Gancedo (Universidad de Sevilla) and Huy Q. Nguyen (University of Maryland), in which we obtained the global well-posedness for the 2D one-phase Muskat problem with arbitrary large Lipschitz...

In this three-part lecture series, we will present a series of works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic mixing and enhanced dissipation properties of a passive tracer subject to the motion of an ergodic Markovian flow of...

The non-resistive electron magnetohydrodynamics (MHD) has some peculiar connection with the Euler equation. Some one-dimensional reduced models are suggested as an attempt to build intuition toward understanding the nonlinear structure and dynamics...