**Seminars and Colloquiums**

for the week of October 19, 2015

for the week of October 19, 2015

*SPEAKER:*

Sam Corson, Vanderbilt, Monday

Delong Li, UTK, Monday

Jan Rosinski, UTK, Tuesday

Zhenlin Guo, UC, Irvine, Wednesday

Nguyen Lam, University of Pittsburgh, Thursday

Kenneth Stephenson, UTK, Thursday

Athma Senthilnathan, UTK, Friday

Chase Worley, UTK, Friday

Alex Freire, UTK, Friday

*Tea Time, Monday - Wednesday, 3:00 pm*

Hosted by Pawel Grzegrzolka

Hosted by Pawel Grzegrzolka

**Monday October 19**

GEOMETRY/TOPOLOGY SEMINAR

TITLE: Some New Results on Peano Continua and N-slenderness

TIME: 2:30 – 3:20pm

ROOM: Ayres 114

SPEAKER: Sam Corson, Vanderbilt

Abstract:Peano continua are spaces which furnish a broad variety of fascinating (counter)examples. Although this is true, there are known restrictions on their fundamental groups. Utilizing classical techniques of descriptive set theory we give some interesting new theorems including a "small-loop compactness theorem”. Using an old technique of Graham Higman, we also give a criterion for n-slenderness which has very general consequences.

ALGEBRA SEMINAR

TITLE: The Unimodular rows and Hermitage rings IV

TIME: 3:35 – 4:25pm

ROOM: Ayres 114

SPEAKER: Delong Li, UTK

Abstract: This is the fourth of a series of four talks whose aim is to present a proof (from a book by T. Y. Lam) of the fact that the polynomial ring in n-variables over a field, is a Hermite ring. Following this talk there will be one or more talks related to a conjecture of Serre.

** Tuesday October 20**

STOCHASTICS SEMINAR

TITLE: Characterization of associated squared Gaussian processes

TIME: 2:10 -3:25pm

ROOM: Ayres 114

SPEAKER: Jan Rosinski, UTK

Abstract: The concept of association of random variables is very useful in probability, statistics, and their applications. The famous open problem to characterize associated Gaussian processes was solved by L. Pitt (1982). We will present a solution to a much newer open problem from 1991, to characterize associated squared Gaussian processes, that was recently obtained by N. Eisenbaum (2014). This solution brings together seemingly unrelated concepts of association, infinite divisibility, FKG inequality of mathematical physics, and Green functions of Markov processes. All necessary definitions and basic facts will be given during the talk.

** Wednesday October 21 **

COMPUTATIONAL & APPLIED MATHEMATICS (CAM) SEMINAR

TITLE: Thermodynamically consistent modeling and computations for multiphase flows.

TIME: 3:35 -4:25pm

ROOM: Ayres 112

SPEAKER: Zhenlin Guo, UC, Irvine

Abstract: In this talk, I will introduce a phase-field model for binary incompressible fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier-Stokes equations with additional stress term, Cahn-Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Some numerical examples for the multiphase flows with and without thermocapillary effects will be presented. The results are compared to the corresponding analytical solutions and existing numerical results as validations for our model.

** Thursday October 22**

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: On some functional and geometric inequalities

TIME: 2:10 – 3:25pm

ROOM: Ayres 114

SPEAKER: Nguyen Lam, University of Pittsburgh

Abstract: In this talk, we will discuss the existence and symmetry of maximizers for a family of Caffarelli-Kohn?-Nirenberg interpolation inequalities and Hardy-Trudinger?-Moser inequalities. Moreover, using suitable transforms, we will derive the exact best constant and extremal functions in some particular classes. This is joint work with Mengxia Dong and Guozhen Lu.

JUNIOR COLLOQUIUM

TITLE: Sphere packing in 2.5 dimensions

TIME: 3:40 – 4:30pm

ROOM: Ayres 405

SPEAKER: Kenneth Stephenson, UTK

Abstract: The densest packing of unit-diameter spheres (i.e. discs) in 2D is hexagonal --- namely, the "penny-packing" wherein every disc is tangent to 6 others. The 3D version of the penny-packing is the "grocer-packing", the configuration you see with oranges stacked on a grocery counter. Around 1600 Kepler conjectured that this grocer-packing is the densest possible in 3D, and after a mere 400 years, Tom Hales, his collaborators, and clever computer work have proven Kepler correct. In this talk we consider packings of unit-diameter spheres in 3D, but now with the side condition that they all be tangent to a fixed cylinder. Taking a cue from history, we focus on hexagonal patterns and speculate on density. However, surprising issues enter the picture and suggest that this new problem hovers somewhere between the 2D and 3D cases --- hence the 2.5D of our title. I will use plenty of pictures and hope to get you to exercise your intuition a little as we see if there's a reasonable conjecture to make.

**Friday October 23**

MATH BIOLOGY SEMINAR

TITLE: Invasion of competing species (chapter 6 of Shigesada book)

TIME: 10:10 – 11:00am

ROOM: Ayres 405

SPEAKER: Athma Senthilnathan, UTK

ANALYSIS SEMINAR

TITLE: Circulant Core Hadamard Matrices

TIME: 2:30- 3:20pm

ROOM: BU 476

SPEAKER: Chase Worley, UTK

Abstract: We will begin by discussing Hadamard matrices with both real and complex entries. After dephasing a Hadamard matrix, we can examine the properties of the core of the matrix. We investigate the Hadamard matrices whose core is circulant. We give examples coming from Number Theory. Then we prove a finiteness result for circulant core Hadamard matrices of size p+1 when p is a prime number.

COLLOQUIUM

TITLE: Two Problems in Geometric Analysis

TIME: 3:35 -4:25pm

ROOM: Ayres 405

SPEAKER: Alex Freire, UTK

Abstract: I will describe motivation and results in two lines of research in differential geometry:

1 - Mean curvature motion of systems of hypersurfaces with constant contact angle;

2 - Inverse mean curvature flow, geometric inequalities and isoperimetric mass.

The common thread connecting these topics is that I have worked them in.

*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 *