**Seminars and Colloquiums**

for the week of February 19, 2018

for the week of February 19, 2018

*SPEAKERS*

**Monday**

Jerzy Dydak, University of Tennessee

**Tuesday**

Bo Gao, University of Tennessee

Theodora Bourni, University of Tennessee

**Wednesday**

Vivian Healey, University of Chicago

Jeahyun Park, University of Tennessee

**Thursday**

Judy Day, University of Tennessee

Yannick Sire, Johns Hopkins University

Ryan Unger, University of Tennessee

**Friday**

Christopher Strickland, University of Tennessee

*TEA TIME -
3:00 pm – 3:30 pm
Monday, Tuesday, and Wednesday: Ayres 401
Hosted by:
Anna Lawson and Betsy Downs
*

**Monday, February 19**

**TOPOLOGY/ GEOMETRY SEMINAR**

TITLE: Ends and simple coarse structures III

SPEAKER: Jerzy Dydak, University of Tennessee

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 112

Abstract coarse structures were introduced by J.Roe. Subsequently, equivalent structures, called large scale structures were introduced by J.Dydak and C.Hoffland. This talk is devoted to a much simpler definition of majority of useful coarse structures (metric, group, C_0, etc). Namely, they are equivalence relations on the set of simple ends of sets equipped with a bounded structure. As an application we show that Gromov boundary of every hyperbolic space is an example of a Higson corona and each Freundenthal compactification is an example of a Higson compactification.

**Tuesday, February 20**

**STOCHASTICS/PROBABILITY SEMINAR**

TITLE: Asymptotics for Brownian motion in Poissonian potential with Riesz kernel

SPEAKER: Bo Gao, University of Tennessee

TIME: 2:10 PM-3:20 PM

ROOM: Ayres 114

The model of Brownian motion in Poissonian potential has been studied a lot in literature. In this talk, we will investigate the quenched long term asymptotics for the Brownian motion in a Poissonian potential with Riesz shape functions.

**GENERAL RELATIVITY SEMINAR**

TITLE: The positive mass theorem in 3 dimensions

SPEAKER: Theodora Bourni, University of Tennessee

TIME: 5:00 PM-6:00 PM

ROOM: Ayres 113

In this talk we will present the first part of the 1979 Schoen-Yau paper and prove that the mass of an asymptotically flat 3 dimensional manifold with a possibly non-empty mean convex boundary is non negative.

**Wednesday, February 21**

**ANALYSIS SEMINAR**

TITLE: Tree Embedding via the Generalized Loewner Equation

SPEAKER: Vivian Healey, University of Chicago

TIME: 2:30 PM-3:20 PM

ROOM: Ayres 112

In its most well-known form, the Loewner equation gives a correspondence between curves in the upper half-plane and continuous real functions (called the “driving function” for the equation). We consider the generalized Loewner equation, where the driving function has been replaced by a time-dependent real measure. In the first part of the talk, we investigate the delicate relationship between the driving measure and the generated hull, specifying a class of discrete random driving measures that generate hulls in the upper half-plane that are embeddings of trees. In the second part of the talk, we consider the probabilistic question of finding the scaling limit of these measures for Galton-Watons trees. We particularly focus on distributions on trees converging to the continuum random tree, and we conclude by describing connections to the complex Burgers equation.

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR**

TITLE: Discrete Gagliardo-Nirenberg inequalities

SPEAKER: Jeahyun Park, University of Tennessee

TIME: 3:35 PM-4:35 PM

ROOM: Ayres 112

In this talk, I will talk about a way of getting a discrete version of Gagliardo-Nirenberg inequalities in a typical finite element setting. More specifically, in a globally continuous piecewise polynomial finite element setting, we can only expect 1st order regularity for a function in the finite element space. We will discuss how to get a discrete Gagliardo- Nirenberg type inequality for the finite element function that involves 2nd order derivative in its continuous counterpart (i.e. the original Gagliardo-Nirenberg inequality).

**Thursday, February 22**

**MATH BIOLOGY SEMINAR**

TITLE: An introduction to the methodology of model predictive control in the context of a biomedical application

SPEAKER: Judy Day, University of Tennessee

TIME: 11:10 AM-12:00 PM

ROOM: Hesler 427

**DIFFERENTIAL EQUATIONS SEMINAR**

TITLE: Asymptotic limits for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces

SPEAKER: Yannick Sire, Johns Hopkins University

TIME: 2:10 PM-3:10 PM

ROOM: Ayres 114

I will describe an asymptotic result on the fractional Allen-Cahn equation involvingthe fractional Laplacian. The limiting interface is a stationary nonlocal minimalsurface. A striking phenomenon is a strong convergence result due to a geometricmeasure theory result by Marstrand.

**GEOMETRIC ANALYSIS SEMINAR**

TITLE: The isoperimetric problem and spherical rearrangements

SPEAKER: Ryan Unger, University of Tennessee

TIME: 5:00 PM-6:00 PM

ROOM: Ayres 113

We show how to decrease the Sobolev norm of a smooth function by spherically rearranging its level sets (Polya-Szego inequality). This is connected to the Euclidean isoperimetric problem and the best constant in the Sobolev inequality.

**Friday, February 23**

**SIAM STUDENT CHAPTER**

Title: Informal chat on career path and research interests

Speaker: Christopher Strickland, University of Tennessee

Time: 12:20 PM-1:00 PM

Room: Ayres 404

Bagels will be provided.

**Faculty Meeting **

TITLE: Faculty Meeting

TIME: 3:30 PM-4:30 PM

ROOM: Ayres 405

*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:**