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# Events for 12/04/2018 from all calendars

## Nonlinear Partial Differential Equations

## Student Working Seminar in Groups and Dynamics

## Colloquium - Jonathan Hermon

## Student/Postdoc Working Geometry Seminar

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Hakima Bessaih, University of Wyoming

**Title:** *Nonlinear PDE's Seminar*

**Abstract:**

Date: Tuesday, December 4, 2018 (please notice this is different date than what we have announced earlier)

Title: Mean field limit of interacting filaments for 3d Euler equation

Abstract: The 3D Euler equation, precisely local smooth solutions of class $H^s$ with $s>5/2$ are obtained as a mean field limit of finite families of interacting curves, the so called vortex filaments, described by means of the concept of 1-currents. This is achieved by first replacing the true Euler equation by a mollified one through the regularization of the Biot-Savart law through a small coefficient $\epsilon$. Families of N interacting curves are considered, with long range mean field type interaction, that depends on the coefficient $\epsilon$. When $N$ goes to infinity, the limit PDE is vector-valued (mollified Euler equation) and each curve interacts with a mean field solution of the PDE.

This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result.

**Time:** 3:50PM - 4:50PM

**Location:** BLOC 506A

**Speaker:** Justin Cantu

**Title:** *Groups generated by bounded automata and tile inflation*

**Abstract:** I will introduce bounded automata and the groups they generate when they are invertible. These groups act on regular rooted trees and give examples of self-similar groups, so we can define the corresponding level n orbital (or Schreier) graphs. We will use tile graphs, which are special subgraphs of level n orbital graphs, and their limits to study the orbital graphs of the group acting on the boundary of the tree.

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Jonathan Hermon, Cambridge University

**Description:** **Title:** Mixing and hitting times - theory and applications.

**Abstract:** We present a collection of results, based on a novel operator maximal inequality approach, providing precise relations between the time it takes a Markov chain to converge to equilibrium and the time required for it to exit from small sets. These refine results of Aldous and Lovasz & Winkler. Among the applications are: (1) A general characterization of an abrupt convergence to equilibrium phenomenon known as cutoff. Specializing this to Ramanujan graphs and trees. (2) Proving that the return probability decay is not geometrically robust (resolving a problem of Aldous, Diaconis - Saloff-Coste and Kozma). (3) Random walk in evolving environment.

**Time:** 5:00PM - 6:00PM

**Location:** BLOC 628

**Speaker:** K. Bari, TAMU

**Title:** *Spherical Varieties*

**Abstract:** Here are notes in case you want to look in advance: https://www-fourier.ujf-grenoble.fr/~mbrion/notes_bremen.pdf

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