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Seminars and Colloquiums
for the week of October 19, 2015


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

Monday October 19

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.

TITLE: The Unimodular rows and Hermitage rings IV
TIME: 3:35 – 4:25pm
ROOM: Ayres 114
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

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

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

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.

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

TITLE: Invasion of competing species (chapter 6 of Shigesada book)
TIME: 10:10 – 11:00am
ROOM: Ayres 405
SPEAKER: Athma Senthilnathan, UTK

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.

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



last updated: February 2016

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