**Seminars and Colloquiums**

for the week of February 22, 2016

for the week of February 22, 2016

*SPEAKER:*

Scott Carter, University of South Alabama, Monday

Xia Chen, UTK, Tuesday

Qiwei Sheng, ORNL, Wednesday

Mustafa Elmas, Ben Levy, Brittany Stephenson, and John Cummings, UTK, Thursday

Ken Stephenson, UTK, Friday

**Monday, February 22nd**

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Moves to Diagrams and the construction of invariants

SPEAKER: Scott Carter, University of South Alabama

TIME: 2:30pm – 3:20pm

ROOM: Ayres 113

Knots, knotted trivalent graphs, knotted handle bodies, knotted surfaces, and knotted foams can be studied from a diagrammatic perspective. There are two aspects of such a theory. First, when do different diagrams represent the same knotting? Second, how can quantities be assigned to the diagrams that are invariant under the moves?

We'll begin the discussion from the more familiar point of view of knotted objects in $3$-dimensions. We'll discuss coloring invariants and the corresponding relations that are imposed. Then we'll look at moves to classically knotted objects as "atomic pieces" of knotted $2$-dimensional objects in $4$-space.

The talk will discuss some of the Roseman moves to the knotted objects and their realizations as cycles in a homology theory that includes both group and quandle homology theory.

**Tuesday, February 23rd **

STOCHASTICS

TITLE: Parabolic Anderson Models

SPEAKER: 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.

**Wednesday, February 24th **

COMPUTATIONAL AND APPLIED MATHEMATICS SEMINAR

TITLE: Differential Approximations of the Radiative Transport Equation in Highly Forward-Peaked Media and Its Applications to Inverse Problems

SPEAKER: Qiwei Sheng, ORNL

TIME: 3:35pm – 4:35pm

ROOM: Ayres 113

Applications of biomedical imaging have increased tremendously in the past decade and have significantly contributed to core conceptual advances in biomedical research. Optical tomography is an emerging optical molecular imaging modality. One of the governing equations in optical tomography is the Radiative Transfer Equation (RTE). It is challenging to solve RTE numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the angular variable, leading to prohibitively large amount of computations. For this reason, various approximations of RTE have been proposed in the literature. In this talk, I will introduce a family of differential approximations of the RTE and its applications to inverse problems arising in optical tomography. Existence of the solutions to the inverse problem and its discontinuous Galerkin approximation are proved. Computer simulations are presented that demonstrate the reliability and effectiveness of the proposed optical tomography model.

**Thursday, February 25th**

GRADUATE STUDENT SEMINAR

TITLE: GS Seminar Spotlight on Biomathematics and Numerical Analysis

SPEAKER: Mustafa Elmas, Ben Levy, Brittany Stephenson, and John Cummings, UTK

TIME: 3:40pm – 4:30pm

ROOM: Ayres G004

We have another excellent 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, February 26th**

ANALYSIS SEMINAR

SPEAKER: Ken Stephenson, UTK

TIME: 2:30 pm - 3:20 pm

ROOM: Ayres 121

*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:**