**Seminars and Colloquiums**

for the week of November 11, 2019

for the week of November 11, 2019

*SPEAKERS*

Monday

Louis Gross, UTK**
**Anna Lawson, UTK

**Tuesday**

Jeremy Siegert, UTK

**Jan Rosinski, UTK**

Margaret Grogan, UTK

**Wednesday**

Jack Ryan, UTK

**Thursday**

Tadele Mengesha, UTK

Maximilian Pechmann, UTK

** Tea Time** -

3:00 pm – 3:30 pm

Monday, Tuesday, & Wednesday

Room: Ayres 401

Hosted by: Amanda Lake Heath

Topics: How to craft a teaching statement; How to shape a research statement; Weekly check-in

**Monday, Nov. 11**

**MATH BIOLOGY SEMINAR
**TITLE: Further Introduction to Complexity Theory

SPEAKER: Louis Gross, UTK

TIME: 10:10 AM

ROOM: Claxton 105 at NIMBioS

Abstract:

**ALGEBRA SEMINAR
**TITLE: Ideal Factorization

SPEAKER: Anna Lawson, UTK

TIME: 3:35 PM

ROOM: Ayres 114

**Tuesday, Nov. 12**

**TOPOLOGY/ GEOMETRY SEMINAR
**TITLE: Inductive Dimension of Coarse Proximity Spaces II

SPEAKER: Jeremy Siegert, UTK

TIME: 11:10-12:25 PM

ROOM: Ayres 114

Abstract: In this talk, we define the asymptotic inductive dimension, $asInd$, of coarse proximity spaces. In the case of metric spaces equipped with their metric coarse proximity structure, this definition is equivalent to the definition of $asInd$ given by Dranishnikov for proper metric spaces. We show that if the boundary of a coarse proximity space is completely traceable, then the asymptotic inductive dimension of the space is equal to the large inductive dimension of its boundary. Consequently the large inductive dimension of well known boundaries such as the Gromov boundary and the visual boundary of Cat($0$) spaces is characterized. We also provide conditions on the space under which the boundary is completely traceable. Finally, we use neighborhood filters to define an inductive dimension of coarse proximity spaces whose value agrees with the Brouwer dimension of the boundary.

**STOCHASTICS/PROBABILITY SEMINAR**

TITLE: Stochastic Dini's theorem with applications (Part 3)

SPEAKER: Jan Rosinski, UTK

TIME: 2:10 PM-3:25 PM

ROOM: Ayres 112

Abstract: A stochastic version of Dini's theorem was found by Ito and Nisio. It provides a powerful tool to deduce the uniform convergence of stochastic processes from their pointwise convergence. Unfortunately, this tool fails in stronger than uniform modes of convergence, such as Lipschitz or phi-variation convergence, the latter mode being natural for processes processes with jumps. In this work we establish a stochastic version of Dini's theorem in a new framework that covers processes with jumps and strong modes of convergence. We apply these results to Levy driven stochastic differential equations**.**

ORAL SPECIALTY EXAM

Speaker: Margaret Grogan, UTK

Time: 3pm

Room: 406A

Her committee consist of Professors Prosper (Chair), Day, and Lenhart.

**Wednesday, Nov. 13**

ANALYSIS SEMINAR

TITLE: An Exploration of Loewner Hull Theory

SPEAKER: Jack Ryan, UTK

TIME: 2:30 PM

ROOM: Ayres 113

Abstract: The Loewner differential equation is a tool that provides a correspondence between compact sets in the closure of the upper half-plane and continuous real-valued functions. In this talk, we will explore some of the natural questions that arise in the study of this theory and provide a brief survey of results that give partial answers to these questions. We will then illustrate a specific example of a continuous function and explore its behavior as it pertains to the relevant questions asked in the first half of the talk.

**Thursday, Nov.14**

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Introduction to nonlocal operators and equations

SPEAKER: Tadele Mengesha, UTK

TIME: 2:10 PM

ROOM: Ayres 112

Abstract: Nonlocal models are becoming commonplace across applications. Typically these models are formulated using integral operators and integral equations, in lieu of the commonly used differential operators and differential equations. In this introductory lecture, I will present main properties of these nonlocal operators and equations. Tools of analyzing them such as nonlocal calculus, methods of showing well posedness of models, as well as corresponding solution/function spaces will be discussed. Behavior of solutions of nonlocal equations as a function of a measure of nonlocality will be analyzed. For example, with proper scaling, we will confirm consistency of models by showing that in the event of vanishing nonlocality, a limit of such solutions solve a differential equation. We will demonstrate all these in two model examples: a nonlocal model of heat conduction and a system of coupled equations from nonlocal mechanics.

**JR. COLLOQUIUM
**TITLE: Bose-Einstein condensation of an Ideal Gas

SPEAKER: Maximilian Pechmann, UTK

TIME: 3:40 PM

ROOM: Ayres 405

Abstract: A Bose-Einstein condensate is a state of matter of a Bose gas and an exotic quantum phenomenon. It was theoretically predicted by Bose and Einstein in 1924, but was long considered a mathematical curiosity without practical use. However, since the experimental observation of such a condensate in 1995, Bose-Einstein condensation is a field of research of great interest. Although this phenomenon is well understood from a physical point of view, its mathematically rigorous description is still incomplete. We present a mathematical precise treatment of the Bose-Einstein condensation in the simple case of an ideal Bose gas in a box.

*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 Dr. Christopher Strickland, cstric12@utk.edu *

**Past notices:**