Monday, March 26, 2007

Topology Seminar

TIME: 10:10a.m. -11:00a.m.
ROOM: Ayres Hall 015
SPEAKER: Andrzej Nagorko
TITLE: “Near-homeomorphisms of Nobeling manifolds”
ABSTRACT: "The n-dimensional Nobeling space \nu^n is a subset of the (2n+1)-dimensional euclidean space that consists of all points with at most n rational coordinates. An n-dimensional Nobeling manifold is a Polish space locally homeomorphic to \nu^n. It is known that these manifolds are n-dimensional analogues of infinite dimensional Hilbert space manifolds. I'll talk about recent joint results with A. Chigogidze concerning near-homeomorphisms of Nobeling manifolds. We proved analogues of theorems of Chapman and Ferry about near-homeomorphisms of Hilbert space and euclidean manifolds."

Applied Math Seminar

TIME: 3:35 p.m. -­ 4:25 p.m.
ROOM: Ayres Hall 309A
SPEAKER: Cheng-Xian (Charlie) Lin, Mechanical, Aerospace, and Biomedical Engineering Dept. University of Tennessee TITLE: Numerical Solution of Navier-Stokes Equations for Engineering Applications
ABSTRACT: Due to the significant advancement in computing infrastructures and the numerical solution of complete Navier-Stokes equations, it has become feasible to tackle many practical engineering problems. In this talk, Dr. Lin will share his research interests in computational fluid dynamics (CFD) from an engineering standpoint. He will give a brief look at the available mathematical models for flows in continuum and non-continuum regimes, and a discussion about verification and validation for modeling flows in both macro and micro scales. Several previously funded research projects will be used to illustrate the applications of CFD in heat exchangers, nuclear waste transport, electronic cooling, and micropropulsion systems.

Tuesday, March 27, 2007

Junior colloquium

TIME: 3:30 p.m. -­ 4:30 p.m.
ROOM: Ayres Hall 214
SPEAKER: Dr. Pavlos Tzermias
TITLE: Things you wanted to know about integrals but were afraid to ask
ABSTRACT: It is a very difficult problem to decide whether an elementary function has an elementary indefinite integral and, if so, how to compute it explicitly. A precise formulation of this problem was given (in 1833) by Liouville who was the first person to prove that certain functions do not have elementary integrals.In recent decades, the general problem was solved thanks to the combined efforts of several mathematicians. In the process, many unexpected connections between diverse mathematical disciplines were revealed and some popular misconceptions about the nature of the problem were debunked. We will discuss these issues as extensively as time permits.

The Junior Colloquium is aimed primarily at undergraduate students, but all are most welcome to attend. Pizza will be served immediately before the talk.

Wednesday March 28, 2007

Analysis Seminar

Time: 3:35p.m.-4:25p.m.
ROOM: Ayres Hall 309A
Speaker: Dr. Michael Frazier Mathematics Department Head
Title: Introduction to Littlewood-Paley Theory
Abstract: We briefly summarize what we covered last semester about the Haar functions and Littlewood-Paley theory. Then we continue with material which is in the same direction, but does not depend on, last semester's material. We begin by talking about different versions of Calderon's formula, including discrete versions which are predecessors of wavelets. We lead up to a unified theory of function spaces and Calderon-Zygmund operators.

Algebra Seminar

TIME: 3:35 p.m. -­ 4:25 p.m.
ROOM: Ayres Hall 309B
SPEAKER: Ryan Clark
TITLE: Ryan Clark will finish speaking on injective modules. Masato Kobayashi and Ben Lynch will start lecturing on modules over Dedekind and Prufer domains.

Special Applied/Computational Math Seminar

TIME: 3:35 p.m. -­ 4:25 p.m.
ROOM: Ayres Hall 218
SPEAKER: Professor Andreas Prohl, University of Tuebingen, Germany
TITLE: Numerical approximations of harmonic map heat flows and wave maps to the sphere
ABSTRACT: The harmonic map heat flow to the sphere is a prototype evolution problem, with many applications in materials science (Landau-Lifshitz equation, Ericksen-Leslie equation, etc.). The main difficulty of space-time discretizations is to conserve the sphere constraint, to eventually construct weak solutions with practical (e.g., finite element) schemes when discretization parameters tend to zero.
In the talk, we discuss (i) discretizations of reformulations of the problem, and (ii) formulations which use discrete Lagrange multipliers. Both cases employ lowest order conforming finite elements, and we show convergence to weak solutions as mesh-parameters tending to zero. The results are then extended to p-harmonic map heat flow, Landau-Lifshitz Gilbert with variants, and wave maps to the sphere.
The results are jointly obtained with J. Barrett (Imperial College, London), S. Bartels (Humboldt University, Berlin), X. Feng (U of Tennessee, Knoxville), and C. Lubich (U of Tuebingen).

Thursday, March 29, 2007

Probability Seminar

TIME: 10:10 a.m. - 11:00 a.m.
ROOM: 309B Ayres Hall
SPEAKER: Professor Vladas Pipiras, UNC - Chapel Hill
TITLE: Adaptive wavelet decompositions of stationary processes
ABSTRACT: The idea of expanding a random process with respect to a basis, often with uncorrelated coefficients, has been ubiquitous in both theory and applications of Probability and Statistics. More recently, wavelets have been considered for such bases due to their good time and frequency-domain localization properties. The classical case of stationary processes, though, still remains to be fully explored under the wavelet framework. In this talk, particular wavelet-based decompositions of (Gaussian) stationary processes are discussed. The expansions exhibit uncorrelated detail (high-frequency) coefficients and possibly dependent approximation (low-frequency) coefficients. The correlation structure of the process enters into the associated (non-orthogonal) wavelet basis. Several examples of Gaussian random processes are considered, such as the Ornstein-Uhlenbeck process and fractionally integrated time series. Applications to simulation and to Maximum Likelihood Estimation with a particular focus on long range dependence are presented.

Friday, March 30, 2007

Colloquium

TIME: 3:35 p.m. – 4:25 p.m.
ROOM: 214 Ayres Hall
SPEAKER: Professor Stephen H. Davis, Engineering Sciences and Applied Mathematics Northwestern University
TITLE: Self-Organization of Quantum Dot
ABSTRACT: When an anisotropic material is deposited layer-by-layer on a substrate, the thin, solid film produced can become unstable due to elastic or thermodynamic effects leading to corrugations that coarsen in scale over time. The 'final state' is a set of pyramidal hills separated by wetting layers. These hills are small enough that they display quantum electrical properties suitable for new-age computing. This lecture concerns the mathematical description of this evolution using asymptotic and numerical analysis. In addition to accurate predictions of coarsening processes, new PDE's are derived that display interesting phenomena such as transitions from coarsening to roughening.

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