Math Calendar
Upcoming Events
Colloquium
Amenability, optimal transport and abstract ergodic theorems- Location- SC 5211
Christian Rosendal, University of Maryland
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.
Subfactor Seminar
Connes rigidity conjecture for groups with infinite center- Location- SC1432
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.
Topology & Group Theory Seminar
Short curves of end-periodic mapping tori – Location – SC1432
Brandis Whitfield – Temple University
A homeomorphism of a infinite-type surface is end-periodic if each of its ends is either attracting or repelling under the map. Surprisingly, the end-periodicity of the map implies that its associated mapping torus is tame, i.e. the interior of a compact manifold. Further, if the map is atoroidal, then its mapping torus admits a hyperbolic structure. As an “infinite type” analogue to work of Minsky in the finite-type setting, we show that given a subsurface Y of S, the subsurface projections between the “positive” and “negative” Handel-Miller laminations provide bounds for the geodesic length of the boundary of Y as it resides in Mf. In this talk, we’ll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic 3-manifolds, show these techniques may be used in the infinite-type setting, and how our main theorems give back results to the closed, fibered setting.
Host: Spencer Dowdall
Talk by Alice Mark
Alice Mark Vanderbilt University Abstract tba
Alice Mark
Vanderbilt University
Abstract tba
PDE Seminar
Small scale creations for 2D free-boundary incompressible Euler equations with surface tension – Location- Sony Building- A1013
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.
Subfactor Seminar
Braided trivalent categories and the Exceptional Series – Location – SC 1432
Noah Snyder, Indiana University
One major topic in planar algebras is to study “simple skein theories” which here “skein theory” means we are looking at planar algebras generated by certain simple diagrams (like trivalent vertices) and “simple” means the dimensions of the box spaces aren’t too big. For example, questions of this kind were studied by Kazhdan-Wenzl (oriented skein theories generated by a 2-box), Wenzl-Tuba (unoriented braided skein theories), Bisch-Jones-Liu (shaded skein theories generated by a 2-box), and Kuperberg and Morrison-Peters-Snyder (skein theories generated by a trivalent vertex). In work joint with Thurston and joint in part with Morrison, we study simple braided trivalent skein theories. It turns out that for generic values of a twist parameter these skein theories are closely related to the conjectural exceptional family of Deligne-Vogel-Cvitanovic. It’s also interesting to look at what happens when this twist parameter is a small root of unity, in which case we see examples in the G2, F4, and S_t families as well as a possible new example at a fifth root of unity.
Topology & Group Theory Seminar
Title: TBA – Location – SC1432
Ryan Dickmann – Vanderbilt
Abstract: TBA
Talk by Mark Ellingham and Rares Rasdeaconu
Vanderbilt University Abstract tba
Vanderbilt University
Abstract tba
Subfactor Seminar
$M_d$ type approximation properties for locally compact groups – Location- SC1432
Bat-Od Battseren, Vanderbilt University
$M_d$ type approximation properties are group approximation properties that are studied in connection to Dixmier’s similarity problem. These properties are known to be stable under measure equivalence, W*-equivalence, and von Neumann equivalence. In this talk, we will discuss how we can define these properties for locally compact second countable groups and show that lattices and their ambient group share the same properties.
Talk by Alex Wright
Alex Wright University of Michigan Abstract tba
Alex Wright
University of Michigan
Abstract tba
Talk by Stephane Jaffard
Stephane Jaffard University Paris Est Creteil Abstract tba
Stephane Jaffard
University Paris Est Creteil
Abstract tba
PDE Seminar
Title- TBA – Location- TBA
Misha Perepelitsa, University of Houston
Abstract: TBA