Ugo Gianazza, University of Pavia (Italy).

Abstract – here.

Christian Rosendal – University of Maryland

Abstract: TBA

Host: Denis Osin

Christian Rosendal, University of Maryland Abstract. The concept of amenability is ubiquitous in functional analysis, group theory and logic. In general, amenability of, for example, a group allows one to integrate bounded real valued functions on the group in a translation invariant manner, which is of great utility in many contexts. However, unbounded functions are…

Christian Rosendal, University of Maryland

Abstract. The concept of amenability is ubiquitous in functional analysis, group theory and logic. In general, amenability of, for example, a group allows one to integrate bounded real valued functions on the group in a translation invariant manner, which is of great utility in many contexts. However, unbounded functions are a completely different matter. Nevertheless, by using tools from the theory of optimal transport, more specifically, optimal transportation cost spaces, we shall present a couple of results that show how one may integrate potentially unbounded Lipschitz functions defined on amenable groups as long as the latter admit no non-trivial homomorphism to the reals. This is related to previous results of Schneider–Thom and Cuth–Doucha in the bounded setting. The talk will be aimed at a general mathematical audience.

Adriana Fernandez I Quero, University of Iowa

• In this paper we propose for study a natural version of Connes Rigidity Conjecture (1982) which involves property (T) groups with infinite center. Using methods at the rich intersection between von Neumann algebras and geometric group theory we provide several instances when this holds. This is joint work with Ionut Chifan, Denis Osin, and Hui Tan.

Brandis Whitfield – Temple University

Abstract: TBA

Host: Spencer Dowdall

Kevin Hu, Duke University

In this talk, I will discuss 2D free boundary incompressible Euler equations with surface tension. We construct initial data with a flat free boundary and arbitrarily small velocity, such that the gradient of vorticity grows at least double-exponentially for all times during the lifespan of the corresponding solution. This work generalizes the celebrated result by Kiselev–Šverák to the free boundary setting. The free boundary introduces some major challenges in the proof due to the deformation of the fluid domain and the fact that the velocity field cannot be reconstructed from the vorticity using the Biot-Savart law. We overcome these issues by deriving uniform-in-time control on the free boundary and obtaining pointwise estimates on an approximate Biot-Savart law. This is joint work with Chenyun Luo and Yao Yao.

Noah Snyder, Indiana University

Abstract: TBA

Dickmann Ryan – Vanderbilt

Abstract: TBA

Bat-Od Battseren, Vanderbilt University

Abstract- TBA

Misha Perepelitsa, University of Houston

Abstract: TBA