**Seminars and Colloquiums**

for the week of April 8, 2016

for the week of April 8, 2016

*SPEAKER:*

Logan Higginbotham, UTK, Monday

Jesse Thorner, Emory University, Monday

Jan Rosinski, UTK, Tuesday

Stefan Schnake, UTK, Wednesday

Jimmy Scott, UTK, Thursday

Josh Mike, UTK, Friday

Evita Nestoridi, Stanford, Friday

*TEA TIME*

3:00 pm – 3:30 pm

Monday, Tuesday, Wednesday

Room: Ayres 401

Hosted By: Pawel Grzegrzolka and Delong Li

**Monday, April 11th **

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Investigating Group Actions on Metric Spaces with Asymptotic Property C

SPEAKER: Logan Higginbotham, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

Let G be a finitely generated group acting transitively by isometries on a metric space M, where M has asymptotic property C. We prove that under a certain condition, G too will have asymptotic property C. If time provides, we will prove a similar result with straight finite decomposition complexity rather than asymptotic property C (with mild conditions).

ALGEBRA SEMINAR

TITLE: The least prime of the form $x^2 + ny^2$

SPEAKER: Jesse Thorner, Emory University

TIME: 3:35pm - 4:25pm

ROOM: Ayres 114

Let $n$ be a positive integer. Studying primes of the form $x^2+ny^2$ (where $x$ and $y$ are integers) naturally leads to several beautiful topics that are ubiquitous in modern number theory, including class field theory and the Chebotarev density theorem. It follows from the Chebotarev density theorem that there are infinitely many primes of the form $x^2+ny^2$; this mirrors the fact that there are infinitely many primes congruent to $a$ modulo $q$ whenever $\gcd(a,q)=1$. However, it is a fairly hard analytic problem to determine how far we must check before we see a prime congruent to $a$ modulo $q$. In this talk, we will discuss how class field theory, the Chebotarev density theorem, and analytic number theory come together to help us to determine how far we must check before we see a prime of the form $x^2+ny^2$.

** Tuesday, April 12th **

STOCHASTICS SEMINAR

TITLE: Isomorphism identities for Poissonian random fields with applications

SPEAKER: Jan Rosinski, UTK

TIME: 2:10pm – 3:25pm

ROOM: Ayres 114

The celebrated Cameron-Martin formula describes how a general Gaussian measure (the distribution of a Gaussian random field or a process) changes under translations by certain functions (elements of the Cameron-Martin space). Therefore, the spaces of functionals of Gaussian random fields with and without translation are isomorphic under the Gaussian measure, and after change of the measure, they are isometric. We give a framework for analogous formulas for Poissonian random fields and discuss some applications.

**Wednesday, April 13th **

COMPUTATIONAL AND APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Interior Penalty, Discontinuous Galerkin, Finite Element Methods for Linear Elliptic PDEs in Non-divergence Form

SPEAKER: Stefan Schnake, UTK

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

This talk will focus on discontinuous Galerkin methods to approximate strong solutions for linear elliptic PDEs in non-divergence form whose coefficients are only continuous. These PDEs present themselves in the nonlinear Hamilton-Jacobi-Bellman equations, which have applications in stochastic optimal control and mathematical finance, as well as the linearization of the Mange-Amprere equations. We introduce a few interior penalty, discontinuous Galerkin, finite element methods which are simple in construction. The highlight of the talk will be to show the stability of these methods through a discrete Calderon-Zygmond estimate. Several numerical tests will be shown towards the end of the talk.

**Thursday, April 14th **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: An Introduction to Schrodinger’s Equation

SPEAKER: Jimmy Scott, UTK

TIME: 2:00pm - 3:00pm

ROOM: Ayres 113

It is accepted as an axiom in quantum mechanics that the trajectories of objects at the atomic level are modeled by solutions to Schrödinger’s Equation. The sense in which the equation models these trajectories will be discussed through the presentation of the classical yet significant case of the hydrogen atom model. Well-posedness and other properties of solutions in the absence of a source term will be presented as well.

** Friday, April 15th **

ANALYSIS SEMINAR

TITLE: An Introduction to quasiconformal mappings and the generalized
Riemann mapping theorem.

SPEAKER: Josh Mike, UTK

TIME: 2:30pm – 3:20pm

ROOM: Ayres 121

As talk 1 of 2, we will introduce the general geometric definition of a conformal mapping and translate this definition into the familiar Cauchy-Riemann equations in the complex numbers. Then, we will do the same for quasiconformal mappings on manifolds and complex numbers.

Groetsch’s problem will be used to motivate the study of quasiconformal mappings and its weak formulation. Finally, the talk will conclude by sketching the compact version of the generalized Riemann mapping theorem. This proof will involve a singular integral operator and a neat geometric series of it. We will loosely follow “Lectures on Quasiconformal Mappings” by Lars Ahlfors (Who, incidentally, won one of the two first fields medals).

COLLOQUIUM

TITLE: Hyperplane arrangements and Stopping times

SPEAKER: Evita Nestoridi, Stanford

TIME: 3:30pm-4:30pm

ROOM: Ayres 405

Consider a real hyperplane arrangement and let C denote the collection of the occurring chambers. Bidigare, Hanlon and Rockmore introduced a Markov chain on C which is a generalization of some card shuffling models used in computer science, biology and card games: the famous Tsetlin library used in dynamic file maintenance and cache maintenance and the riffle shuffles are two important examples of hyperplane walks. I introduce a strong stationary argument for this Markov chain, which provides explicit bounds for the separation distance. I will try to explain both the geometric and the probabilistic techniques used in the problem.

*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:**

3/14/2016 - spring break