### Seminars and Colloquiums 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
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
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:

Nov. 4, 2019

Oct. 28, 2019

Oct. 21, 2019

Oct. 14, 2019

Oct. 7, 2019

Sept. 30, 2019

Sept. 23, 2019

Sept. 16, 2019

Sept. 9, 2019

Sept. 2, 2019

Aug. 26, 2019

2018-19

2017-18

###### last updated: November 2019

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu