Seminars and Colloquiums
for the week of February 22, 2016
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
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
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