Seminars and Colloquiums
for the week of March 7, 2016
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
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
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.
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
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
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