Seminars and Colloquiums
for the week of September 30, 2019
Maximilian Pechmann, UTK
Jeahyun Park, UTK
Paul McAnear, UTK
Mat Langford, UTK
Pavan Turaga, Arizona State University
Liet Vo, UTK
Li Chen, Univ of Connecticut
Dustin Cartwright, UTK
3:00 pm – 3:30 pm
Monday, Tuesday, & Wednesday
Room: Ayres 401
Hosted by: Hannah Thompson
Topics: How to stay on track with your research/how to quantify progress; Things to expect before, during, and after an oral exam; Weekly check-in
Tuesday, October 1
PROBABILITY AND STOCHASTICS SEMINAR
TITLE: Bose-Einstein condensation in random potentials – Pt. 3
SPEAKER: Maximilian Pechmann, UTK
TIME: 2:10 PM
ROOM: Ayres 112
Abstract: It is known that random potentials can enhance the occurrence of some type of condensate in Bose gases. With the exception of a few special cases, it is, however, unclear whether such a condensation is actually a Bose-Einstein condensation (BEC). After introducing the definition of BEC, we discuss the results that are known so far concerning the occurrence of BEC in noninteracting Bose gases that are placed in random potentials. We introduce the Luttinger-Sy model (LSM), which is a central model in this research area and one of the very few random models for which the occurrence of BEC has been rigorously proved. Very recently, the occurrence of BEC has also been shown for a generalization of the LSM, and we discuss the main idea of the proof. Lastly, we give an overview of the case where the particles of the Bose gas interact with each other.
Wednesday, October 2
COMPUTATIONAL & APPLIED MATH SEMINAR
TITLE: An ODE model for Nesterov’s accelerated gradient descent method for Lipschitz smooth, strongly convex objective functionals
SPEAKER: Jeahyun Park, UTK
TIME: 3:35 PM
ROOM: Ayres 112
Abstract: In 1983, Nesterov devised a scheme (accelerated gradient descent method or AGD) that accelerates the convergence of the good old gradient descent method (GD) for minimizing an objective function. This scheme has recently attracted the interest of many researchers in the current boom of statistical learning since its first-order nature makes it suitable for dealing with large scale data. Many researchers have worked on how to generalize or improve AGD to make it even faster. However, it has not been clear why the acceleration works since Nesterov's analysis uses an abstract technique, called estimating sequence, which has made it hard to generalize or improve AGD. Recently, several approaches to the 'why' direction have been taken and have explained why for some cases, but the question "why does AGD exhibit an accelerated exponential convergence when the objective function is strongly convex and Lipschitz smooth?" has remained unanswered. In this talk, we will talk about the answer to this question by interpreting AGD as a discretization of a second-order ODE.
Thursday, October 3
AWM & SACNAS LUNCHEON
TITLE: Imposter Syndrome
SPEAKER: Paul McAnear, Director, Student Counseling, UTK
TIME: 11:30 am
ROOM: Ayres 308H
DIFFERENTIAL EQUATIONS SEMINAR
TITLE: Concavity of the arrival time II
SPEAKER: Mat Langford, UTK
TIME: 2:10 PM-3:25 PM
ROOM: Ayres 112
Abstract: A natural question that arises in the study of elliptic and parabolic PDE asks “when is the solution to a given problem a concave function?”. A related question concerns the convexity of the level sets of a solution. Of course, whereas a function is concave only if its level sets are convex, the converse is certainly not true. In my previous talk, I presented a beautiful argument, discovered in the '80s by N. Korevaar, which demonstrates the concavity of solutions to a very large class of problems. In this talk, I will focus on certain curvature flow equations; I will show how Korevaar’s argument can be modified to obtain a sharp power-concavity property of the time-of-arrival function, and explain why this is interesting. The content of this talk is joint work with Theodora Bourni.
MATH DATA SCIENCE SEMINAR
TITLE: Geometric methods in computer vision and movement analysis
SPEAKER: Pavan Turaga, Arizona State University
TIME: 2:10 PM-3:10 PM
ROOM: Ayres 111
Abstract: In this talk, we will discuss problems involving activity and scene analysis, where we motivate the need for mathematical approaches rooted in differential geometry and topology. We discuss recent work in non-linear dynamical analysis as applied to human activity modeling where we propose to characterize dynamical attractors via their geometric and topological properties. We demonstrate results on activity recognition and scene analysis problems where these methods provide a well-grounded general purpose framework. These methods are shown to work well in a variety of different dynamical time-series databases with minimal changes to the underlying framework. We also present preliminary interdisciplinary work and emerging opportunities at the intersection of geometric computing and real-time interactive feedback systems for mobility and balance-related disorders.
ORAL SPECIALTY EXAMINATION
Speaker: Liet Vo, UTK
Time: 3:30 pm
Room: Ayres 124
His committee consist of Professors: Feng (Chair), Chen, Karakashian, and Salgado.
GEOMETRIC ANALYSIS SEMINAR
TITLE: BV functions and isoperimetry on Dirichlet spaces
SPEAKER: Li Chen, Univ of Connecticut
TIME: 4:00 PM
ROOM: Ayres 111
Abstract: I present a theory of BV functions on Dirichlet spaces, focusing on the strictly local case with Gaussian heat kernel bounds and the strongly local case with sub-Gaussian heat kernel bounds. Under weak Bakry-Emery curvature type conditions, we prove global isoperimetric inequalities.
Friday, October 4
TITLE: Algebraic Matroids and the Lindström Valuation
SPEAKER: Dustin Cartwright, UTK
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: An algebraic matroid is a combinatorial object which encodes the algebraic relations among elements in a field, or, equivalently, dimensions of projections of an algebraic variety. Algebraic matroids have been difficult to study, but I will talk about recent developments of matroid flocks and the Lindström valuation, which give a new way to study algebraic matroids by their linearizations. I will discuss an important class of examples coming from one-dimensional algebraic groups.
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, email@example.com