**Seminars and Colloquiums**

for the week of October 23, 2017

for the week of October 23, 2017

*SPEAKERS*

Wlodek Bryc, University of Cincinnati, Tuesday

Abner Salgado, UTK, Wednesday
**
**Jerzy Dydak, UTK, Wednesday

Ryan Unger, Thursday

Dr. Yen-Chi Chen, University of Washington, Friday

*TEA TIME*

*3:00 pm – 3:30 pm
Monday, Tuesday,
Wednesday
Ayres 401
Hosted By: *Anna Sisk & Samantha Clapp

**Tuesday October 24, 2017**

**STOCHASTICS/ PROBABILITY SEMINAR**

TITLE: Fluctuations for particle density of Asymmetric Simple Exclusion Process

SPEAKER: Wlodek Bryc, University of Cincinnati

TIME: 2:10-3:25pm

ROOM: Ayres 113

The asymmetric simple exclusion process (ASEP) with open boundaries is one of the most widely investigated models for open non-equilibrium systems in the physics literature. I will present the model, and discuss some recent results obtained in joint papers with Jacek Wesolowski and with Yizao Wang.

** Wednesday October 25, 2017**

**ANALYSIS SEMINAR**

TITLE: How analysis can save your numerics

SPEAKER: Abner Salgado

TIME: 2:30-3:20pm

ROOM: Ayres 113

In this talk I will show how some results from real and harmonic analysis have helped me in the development and understanding of numerical schemes. I will focus on two cases: The control of PDEs at points and the numerics for fractional differential equations.

** TOPOLOGY/ GEOMETRY SEMINAR
**TITLE: Profinite structures on residually finite groups II

SPEAKER: Jerzy Dydak, UTK

TIME: 3:35-4:25 PM

ROOM: Ayres 405

Given a countable group $G$ one can put a large scale (coarse) structure on it by selecting an increasing sequence $\{F_n\}_{n\ge 1}$ of finite subsets of $G$ whose union is $G$ and declaring a cover $\mathcal{U}$ of $G$ to be uniformly bounded if and only if there is $n\ge 1$ such that $\mathcal{U}$ refines $\{g\cdot F_n\}_{g\in G}$. It is well-known and easy to show that the coarse structure obtained that way is unique and is equal to the bounded metric structure given by any word metric on $G$ if $G$ is finitely generated.

In this talk we consider a dual situation in case of residually finite countable groups $G$. Given a decreasing sequence $\{G_n\}_{n\ge 1}$ of subgroups of $G$ of finite index whose intersection consists of the neutral element $e_G$ only, we define a small scale (uniform) structure on $G$ (which we call a profinite structure on $G$) by declaring a cover $\mathcal{U}$ of $G$ to be uniform if and only if there is $n\ge 1$ such that $\{g\cdot G_n\}_{g\in G}$ refines $\mathcal{U}$. One can give a characterization of profinite structures on $G$ in terms of topological group structures on $G$.

A natural question is if profinite structures are unique on countable groups. It turns out the answer is no. However, in case of finitely generated residually finite groups $G$ there is only one profinite structure.

This is joint work with Joanna Furno (University of Houston) and James Keesling (University of Florida).

** Thursday, October 26th**

**GEOMETRIC ANALYSIS SEMINAR
**TITLE: The Yamabe Problem I

SPEAKER: Ryan Unger,

TIME: 5-6pm

ROOM: Ayres 113

In 1960 H. Yamabe conjectured that, given a compact Riemannian manifold, there exists a conformal deformation of the metric to one of constant scalar curvature. The combined works of Yamabe, N. Trudinger, T. Aubin, and R. Schoen gave an affirmative solution in 1984. Here we review Yamabe's original paper and give the proof of Yamabe's conjecture in the case when the Yamabe energy is nonpositive.

**Friday, October 27th**

**COLLOQUIUM**

TITLE: Density Tree and Density Ranking in Singular Measures

SPEAKER: Dr. Yen-Chi Chen, University of Washington

TIME: 3:30-4:30pm

ROOM: Ayres 405

A density tree (also known as a cluster tree of a probability density function) is a tool in topological data analysis that uses a tree structure to represent the shape of a density function. Even if the density function is multivariate, a density tree can always be displayed on a two-dimensional plane, making it an ideal tool for visualizing the shape of a multivariate dataset. However, in complex datasets such as GPS data, the underlying distribution function is singular so the usual density function and density tree no longer exist. To analyze this type of data and generalize the density tree, we introduce the concept of density ranking and ranking tree (also called an $\alpha$-tree). We then show that one can consistently estimate the density ranking and the ranking tree using a kernel density estimator. Based on the density ranking, we introduce several geometric and topological summary curves for analyzing GPS datasets.

*If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar. *

*If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu *

**Past notices:**