Un of Tenn | Math Department

Seminars and Colloquiums
for week of November 14, 2011

Speaker:

Prof. Luis Finotti, Monday
Calistus Ngonghala, NIMBioS postdoc, Monday
Prof. Jan Rosinski, Monday
Christine Dumoulin & Tara Kemfort, Thursday
Prof. Remus Nicoara, Thursday
Prof. Steve Wise, Friday

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. Judy Day.

Monday, November 14

ALGEBRA SEMINAR
TIME: 2:30 - 3:20 p.m.
ROOM: Ayres B004
SPEAKER: Prof. Luis Finotti
TITLE: Construction of Witt Vectors
ABSTRACT: We will first quickly finish with our overview of p-adic numbers, and then proceed with the construction of Witt vectors. The ring of Witt vectors has similar properties to those of p-adic rings (and their unramified extensions) and in fact generalize those rings. Their structure also introduces some geometry in algebraic problems. On the other hand, computations with these vectors can be extremely difficult. Time permitting, we will discuss how to obtain some improvements in those computations.

DE/APPLIED and COMPUTATIONAL CHRISTINE DUMOULIN & TARA KEMFORT SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 113
SPEAKER: Calistus Ngonghala, NIMBioS postdoc
TITLE: Extreme Multi-stability in a Chemical System

PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 122
SPEAKER: Prof. Jan Rosinski
TITLE: Ito-Nisio Theorem in Skorohod space. Part 2: The result.
ABSTRACT: The Ito-Nisio Theorem implies that various series expansions of Brownian motion converge uniformly pathwise with probability one. This was the original motivation for the theorem in C[0,1]. We prove the corresponding result for series expansions of sample discontinuous processes, for which the natural setting is Skorohod space D[0,1]. Our result gives a tool to analyze jump structures of discontinuous processes in a general non-Markovian setting. The talk is based on a joint work with Andreas Basse-O'Connor.

Thursday, November 17

MATH BIOLOGY SEMINAR
TIME: 12:45 – 1:35 p.m.
ROOM: NIMBioS Classroom
SPEAKERS: Christine Dumoulin & Tara Kemfort
TITLE: Spatial Dynamics in Temporal and Spatial Domains

JUNIOR COLLOQUIUM
TIME: 3:35 – 4:25
ROOM: Ayres 405
SPEAKER: Prof. Remus Nicoara
TITLE: Google's Secret
ABSTRACT: Everybody knows that Google Inc.'s innovations in search technology made it the No. 1 search engine in the world. Google made public their US patent, which reveals a great deal of how they search and rank web sites. We unveil some of the mathematics behind Google's success: graphs, matrices, eigenvalues and eigenvectors, and deep results such as the Perron-Frobenius theorem. We will also discuss other search tools such as Bing, WolframAlpha and Siri.

Pizza will be available at 3:15 p.m.

Friday, November 18

COLLOQUIUM
TIME: 3:35 – 4:25 pm
ROOM: Ayres 405
SPEAKER: Prof. Steve Wise
TITLE: PDE/Numerical Analyses and Computations of some Diffuse Interface Models of Viscous Two-Phase Flows
ABSTRACT: Diffuse interface methods approximate the separating boundary between two fluid phases using an order parameter u that continuously, and usually monotonically, varies from one value in phase A, say u=+1, to another value in phase B, say u=–1, in a boundary layer of small, but finite, thickness. This is in contrast to a sharp interface formulation that would employ a characteristic (or indicator) function description. In the diffuse interface approximation, the "location" of the interface can be identified, though somewhat arbitrarily, as the level surface u=0. In many two-phase fluids, such a diffuse description of an interface is physically justified. In fact, van der Waals had argued that this is the case in the late 19th century, well before the computational significance could be appreciated. Today, however, the diffuse description is typically used as a mathematical formalism (an approximation), and the thickness of the boundary layer is significantly larger than is physically realistic. The smaller the interface thickness is, the smaller the associated approximation error is. I will describe 2 rather simple two-phase flow models, one of which was motivated by my interest in porous media flow and tumor growth, and another of which was motivated by problems in micro-fluidics, lava lamps, and bio-films. Both are close relatives to the well-known Cahn-Hilliard-Navier-Stokes equation. I will discuss some PDE theory, numerical analyses, and computational issues related to both models and will show some 2 and 3d computational results.

This is joint work with X. Feng, O. Karakashian, some students here at UTK, and a few others.

Refreshments will be available in Ayres 401 at 3:15 p.m.

Past notices: