**Seminars and Colloquiums**

for the week of October 30, 2017

for the week of October 30, 2017

*SPEAKERS*

Xia Chen, UTK, Tuesday

Andrew Starnes, UTK, Wednesday
**
**Vincent Heninburg, UTK, Wednesday

Jeremy Seigert, UTK, Wednesday

Prof. Ryan Hynd, University of Pennsylvania, Thursday

Dr. Christopher Strickland, UTK, Thursday

Ryan Unger, Thursday

Professor Jie Shen, Purdue University, Friday

*TEA TIME*

*3:00 pm – 3:30 pm
Monday, Tuesday,
Wednesday
Ayres 401
Hosted By: Alex Lacy & Alec Lewald*

**Tuesday, October 31st **

**STOCHASTICS/ PROBABILITY SEMINAR**

TITLE: Solving Parabolic Anderson with rough and critical Gaussian noise

SPEAKER: Xia Chen, UTK

TIME: 2:10-3:25pm

ROOM: Ayres 113

An important class of the parabolic Anderson equations are the ones with Gaussian noise given as the formal derivative of a fractional Brownian sheet. In this talk we consider the cases (1) when the fractional noise has rough components (i.e., the components with Hurster parameters less than half); (2). When the fractional noise produces only local solution.

Some unsolved problems will be mentioned.

** Wednesday, November 1st **

**ANALYSIS SEMINAR**

TITLE: The Loewner Equation via Examples

SPEAKER: Andrew Starnes, UTK

TIME: 2:30-3:20pm

ROOM: Ayres 113

The Loewner equation gives a correspondence between real functions and sets in the complex plane. In this talk, we will introduce the Loewner equation and look at several examples of this correspondence. After this, we will see some applications of the Loewner equation. Finally, we will discuss simulation methods of the Loewner equation. This talk will be accessible to graduate students who are currently enrolled or have taken real analysis.

** COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR
**TITLE: Filtered Discrete Ordinates Equations

SPEAKER: Vincent Heninburg, UTK

TIME: 3:35-4:25pm

ROOM: Ayres 113

We develop a method to solve the radiative transport equation, in which we introduce a filtered term as a modification to the Discrete Ordinates (or $S_N$) Equations. Under certain conditions the $S_N$ method is known to create non-physical defects, referred to as “ray-effects”, in which the discrete ordinates leave an imprint on the numerical solution, appearing as a spatial distortion. We show that using this modification of the $S_N$ method greatly reduces the occurrence of “ray-effects” in the numerical solution. We present analysis of the method to determine under what conditions under which the numerical solution converges to the true solution. Moreover, to demonstrate the effectiveness of the method, numerical results to certain benchmark problems are shown.

**TOPOLOGY/ GEOMETRY SEMINAR
**TITLE: Deviancy of Coarse Spaces

SPEAKER: Jeremy Siegert, UTK

TIME: 3:35-4:25pm

ROOM: Ayres 405

Coarse embeddings became a topic of great interest after it was proven by Yu that groups admitting a coarse embedding into Hilbert space satisfy the Novikov conjecture. In this talk we will describe a fairly simple means of measuring how much a coarse map between metric (and more generally coarse) spaces “deviates” from being a coarse embedding. We then extend the idea to measuring how much a particular space can “deviate” from being coarsely embeddable in another space. In the process we will describe a class of coarse invariants.

** Thursday, November 2nd **

**DIFFERENTIAL EQUATIONS SEMINAR
**TITLE: Partial regularity for doubly nonlinear parabolic systems

SPEAKER: Prof. Ryan Hynd, University of Pennsylvania

TIME: 2:10-3:10pm

ROOM: Ayres 114

We will present a regularity result for solutions of a PDE system which is a model for general doubly nonlinear evolutions. The system we focus on a particular case of a general class of flows that arise in the study of phase transitions.

** JR. COLLOQUIUM
**TITLE: Zombie Attack! Modeling the Dynamics of a Zombie Apocalypse

SPEAKER: Dr. Christopher Strickland, UTK

TIME: 3:40-4:35pm

ROOM: Ayres 405

In this talk, I present several differential equation models for zombie invasion and analyze them to determine the fate of mankind. Largely based off the 2009 paper "When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection" by Munz et al., this talk will serve as an introduction to epidemiological modeling and present basic dynamical systems analysis for nonlinear systems. It will be of particular interest to any students currently taking MATH 231 or especially MATH 431, since the simplest zombie model is easily analyzed by hand and can serve as an example of Jacobian eigenvalue/eigenvector methods. There will also be plenty of zombie pictures. Like this one.

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

SPEAKER: Ryan Unger

TIME: 5-6pm

ROOM: Ayres 404

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. Here we discuss the resolution of the conjecture in the case when the Yamabe energy is positive. This case has a surprising connection to the positive mass theorem in general relativity.

** Friday, November 3rd **

**COLLOQUIUM
**TITLE: A new and robust approach to construct energy stable numerical schemes for gradient flows

SPEAKER: Professor Jie Shen, Purdue University

TIME: 3:30-4:30pm

ROOM: Ayres 405

In this talk I shall present a new technique, the single auxiliary variable (SAV) approach, to deal with nonlinearities in a large class of gradient flows. The technique is not restricted to specific forms of the nonlinear part of the free energy, it leads to linear and unconditionally energy stable second-order (or higher-order with weak stability conditions) numerical schemes which only require solving decoupled linear equations with constant coefficients. Hence, these numerical schemes are very efficient as well as accurate. We apply the SAV approach to deal with several challenging applications which can not be easily handled by existing approaches, and present numerical results to show that the new schemes are not only more efficient and easy to implement, but also can better capture the physical properties in these models.

*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:**