**Seminars and Colloquiums**

for the week of March 7, 2016

for the week of March 7, 2016

*SPEAKER:*

Dr. Kyle Austin, Ben Gurion University of the Negev (Israel), Monday

Dr. Xia Chen, UTK, Tuesday

David Krieg, Freiberg, Germany, Tuesday

Ahmed Mohammed, Ball State University, Thursday

Eddie Tu and Tyler Massaro, UTK, Thursday

Noel J. Walkington, Carnegie Mellon University, Friday

TEA TIME

3:00 pm – 3:30 pm

Monday, Tuesday, & Wednesday

Room: Ayres 401

Hosted By: Maggie Wieczorek and Kylie Berry

**Monday, March 7th **

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Coarse Dimension Raising and the Higson Corona Functor

SPEAKER: Dr. Kyle Austin, Ben Gurion University of the Negev (Israel)

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

Takahisa Miyata and Ziga Virk introduced a version of n-to-1 maps in large scale geometry and prove various analogues of the classical dimension raising theorems. They prove the following variant of the Hurewicz dimension raising theorem for asymptotic dimension (asdim): If f:X? Y is coarse and coarsely n-to-1 then asdim(Y) ? (asdim(X) + 1)n -1.

Recall that the classical Hurewicz dimension raising theorem is much stronger: If f:X? Y is a closed n-to-1 map of metric spaces then dim(Y) ? dim(X) + (n -1). It has been a matter of some debate since the aforementioned publication as to whether the estimate of Miyata and Virk can be sharpened to be the same as the classical version. This is exactly what Z. Virk and I managed to prove: If f:X? Y is coarse and coarsely n-to-1 then asdim(Y) ? asdim(X) + (n -1). Moreover, our proof relies on the classical Hurewicz theorem via the Higson compactification.

In my talk, I plan to give a brief introduction to all the necessary prerequisite materials to understanding the result, as well as an outline of the proof.

**Tuesday, March 8th**

STOCHASTICS SEMINAR

TITLE: Parabolic Anderson Models: Part 2

SPEAKER: Dr. Xia Chen, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

This will be an introductory talk about the Parabolic Anderson equation with random potential mostly Gaussian noise). The list of the topics includes: motivations, meaning(s) of the solution, and large scale behavior. The targeted audience: graduate students and whoever wants to learn some basic things about the Parabolic Anderson models.

ANALYSIS SEMINAR

TITLE: A discrete version of Carathéodory's Theorem

SPEAKER: David Krieg, Freiberg, Germany

TIME: 3:40pm – 4:30pm

ROOM: Ayres 112

In the second talk an extended setting for circle packings is introduced. Now circles are allowed to regenerate (have radius zero) and to have a more general complex (circle "agglomerations"). Moreover not only Jordan domains but arbitrary bounded, simply connected domains are packed. After briefly sketching the concept of prime ends, I explain how it is possible to get uniqueness results similar to those proven before by using such prime ends. Afterwards existence statements are proven, which finally leads us to a discrete version of Carathéodory's Theorem. This provides the existence and uniqueness of discrete conformal mappings under weak assumptions.

**Thursday, March 10th **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Harnack Inequality for Non-divergence Structure Semi-linear Elliptic Equations

SPEAKER: Ahmed Mohammed, Ball State University

TIME: 2:00pm - 3:00pm

ROOM: Ayres 113

In this talk we will discuss a Harnack inequality for non-negative solutions of $Lu=f(u)$, where $L$ is a non-divergence structure uniformly elliptic operator and $f$ is a non-decreasing function that satisfies appropriate growth conditions at infinity.

GRADUATE STUDENT SEMINAR

TITLE: GS Seminar Spotlight on Probability and Statistics

SPEAKER: Eddie Tu and Tyler Massaro, UTK

TIME: 3:40pm-4:30pm

ROOM: Ayres G004

In the final installment of the GS Seminar Spotlight Series, we take a look at UTK Probability and Statistics, as well as the UTK Intercollegiate Graduate Statistics Program (IGSP), which gives all math graduate students the opportunity to seek a minor or MS in Statistics while they pursue their PhD. We have a stellar panel who will share their experiences picking out classes; taking prelims; choosing an advisor; and much more! Plus, they will field any questions that you may have about moving into one of these areas during your time as a graduate student at UTK.

**Friday, March 11th**

COLLOQUIUM

TITLE: Multiphase Flow: Modelling, Mathematics, Mechanics, and Numerics

SPEAKER: Noel J. Walkington, Carnegie Mellon University

TIME: 3:35pm – 4:25pm

ROOM: Ayres 405

As with many models of complex physical phenomena, the mathematical theory for the equations describing flow of multiphase fluids is incomplete, yet their numerical approximation within the engineering and scientific computing disciplines is ubiquitous. In this context mathematics provides an essential foundation to facilitate the integration of phenomenology and physical intuition with computational algorithms so that codes inherit essential physical and mathematical properties of the underlying problem.

This talk will illustrate how modelling, mechanics, thermodynamics, and thought experiments, can combined to provide insight into models of multiphase fluid flow and their mathematical properties.

*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:**