**Seminars and Colloquiums**

for the week of September 9, 2019

for the week of September 9, 2019

*SPEAKERS*

**Monday
**Lou Gross, UTK

Organizational Meeting, Algebra

**Wednesday**

Vyron Vellis, UTK

Jea-Hyun Park & Tricia Phillips, UTK

**Thursday**

Deborah Kunkel, Clemson University

Maxim Olshanskii, University of Houston

**Tea Time -
**3:00 pm - 3:30 pm

Tuesday & Wednesday

Room: Ayres 401

Hosted by: Anna Sisk & Wencel Valega

Topics: Discussing how mentorships programs are going; How to get involved with the Math Department; Weekly check-in.

**Monday, September 9**

**MATHEMATICAL BIOLOGY SEMINAR
TITLE:** Overview of Game Theory as a Mathematical Theory of Everything

**SPEAKER:**Lou Gross, UTK

**TIME:**10:10 - 11:00 am

**ROOM:**Claxton 105

**ALGEBRA SEMINAR
TITLE:** Organizational meeting

**SPEAKER:**

**TIME:**3:35 PM-4:20 PM

**ROOM:**Ayres 114

Especially important for students registered for 559/659.

**Wednesday, September 11**

** ANALYSIS SEMINAR
TITLE:** A fractal traveling salesman

**SPEAKER:**Vyron Vellis, UTK

**TIME:**2:30 PM

**ROOM:**Ayres 113

**Abstract:**The traveling salesman problem, one of the most renowned problems in computer science, asks for the shortest path that passes through a given finite set of points E in the Euclidean space. What if the set E is infinite? Can we still visit all of its points in finite time? Even more generally, given an arbitrary set E in the space (possibly a fractal), when is it possible to construct a nice map (Holder, Lipschitz) from the unit interval�that contains E in its image? In this talk we discuss this generalized traveling salesman problem which has been a very active field of research in geometric measure theory in the last 30 years.

**COMPUTATIONAL & APPLIED MATH SEMINAR**

**TITLE:** Nesterov Acceleration (Park)

A DATA-driven Approach to Modeling the Herion and Fentanyl Epidemic (Phillips)

**SPEAKER:** Jea-Hyun Park, UTK and Tricia Phillips, UTK

**TIME:** 3:35 PM

**ROOM:** Ayres 112

**Abstract:** (*Park*) 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 20-minute talk, we will talk about how we can improve AGD by introducing a preconditioner. And later this semester, in another 40-minute talk, we will talk about the answer to the aforementioned, quotation marked question by interpreting AGD as a discretization of a second-order ODE.

(*Phillips*) A preliminary report will be given on the formulation and analysis of a heroin/fentanyl epidemic model. This model, consisting of a system of ordinary differential equations, aims to better understand the dynamics between prescription opioid use, prescription opioid addiction, heroin/fentanyl addiction, and recovery from opioid addiction.

**Thursday, September 12**

**MATH DATA SCIENCE SEMINAR**

**TITLE:** Anchored Bayesian Gaussian mixture models

**SPEAKER:** Deborah Kunkel, Clemson University

**TIME:** 2:10 PM-3:10 PM

**ROOM:** Ayres 111

**Abstract:** We present a Bayesian framework for inference on finite Gaussian mixtures in which a few observations, called anchor points, are pre-classified to specific mixture components. This strategy addresses two fundamental challenges that arise in Bayesian mixture models: label-switching under an exchangeable prior specification and the need to specify proper priors for the component-specific parameters. We present the key properties of the anchored model and show that a small number of pre-classified points can alleviate the label-switching problem. The anchor points may be viewed as inducing a data-dependent prior on the features of the mixture components. This perspective motivates a modeling strategy wherein anchor points are used to enforce prior notions about the nature of heterogeneity in the population, bypassing the need to specify prior information about the locations and scales of the mixture components. We describe several methods for automatic selection of the anchor points founded on principles from case influence diagnostics and semi-supervised learning.

**CAM & DIFFERENTIAL EQUATIONS SEMINAR** (Joint Seminar)

**TITLE:** Numerical modelling of lateral phase separation on evolving surf

**SPEAKER:** Maxim Olshanskii, Univ of Houston

**TIME:** 2:10 PM-3:25 PM

**ROOM:** Ayres 112

**Abstract:** We discuss a model of lateral phase separation in a two component thin
material layer, a prototypical problem for understanding spinodal
decomposition and pattern formation observed in biological membranes,
e.g., lipid bilayers. The modelling part leads to a fourth order
nonlinear PDE that can be seen as the Cahn-Hilliard equation posed on
a time-dependent surface. Elementary tangential calculus and the
embedding of the surface in R^3 are used to formulate the model,
thereby facilitating the development of a fully Eulerian
discretization method to solve the problem numerically. We discuss a numerical approach based on geometrically unfitted finite element
spaces. The method avoids any triangulation of the surface and uses a
surface-independent ambient mesh to discretize the equation, and so
the method is capable to handle implicitly defined surfaces and
surfaces undergoing strong deformations and topological transitions.
The talk will be illustrated with animated computations of pattern
formation on a number of steady and evolving shapes, including
examples with merging and splitting spheres.

*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:**