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Series: Analysis Seminar

In this talk, I will discuss some results obtained in my Ph.D. thesis.
First, the point mass formula will be introduced. Using the formula, we
shall see how the asymptotics of orthogonal polynomials relate to the
perturbed Verblunsky coefficients. Then I will discuss two classes of
measures on the unit circle -- one with Verblunsky coefficients \alpha_n -->
0 and the other one with \alpha_n --> L (non-zero) -- and explain the
methods I used to tackle the point mass problem involving these measures.
Finally, I will discuss the point mass problem on the real line. For a long
time it was believed that point mass perturbation will generate
exponentially small perturbation on the recursion coefficients. I will
demonstrate that indeed there is a large class of measures such that that
proposition is false.

Series: Analysis Seminar

Given an "infinite symmetric matrix" W we give a simple condition, related
to the shift operator being expansive on a certain sequence space, under
which W is positive. We apply this result to AAK-type theorems for
generalized Hankel operators, providing new insights related to previous
work by S. Treil and A. Volberg. We also discuss applications and open
problems.

Wednesday, October 14, 2009 - 13:00 ,
Location: Skiles 269 ,
Edson Denis Leonel ,
Universidade Estadual Paulista, Rio Claro, Brazil ,
Organizer:

Fermi acceleration is a phenomenon where a classical particle canacquires unlimited energy upon collisions with a heavy moving wall. Inthis talk, I will make a short review for the one-dimensional Fermiaccelerator models and discuss some scaling properties for them. Inparticular, when inelastic collisions of the particle with the boundaryare taken into account, suppression of Fermi acceleration is observed.I will give an example of a two dimensional time-dependent billiardwhere such a suppression also happens.

Series: Other Talks

We will briefly review the definition of the Cech cohomology groups of a sheaf (so if you missed last weeks talk, you should still be able to follow this weeks), discuss some basic properties of the Cech construction and give some computations that shows how the theory connects to other things (like ordinary cohomology and line bundles).

Series: Research Horizons Seminar

Image segmentation has been widely studied, specially since Mumford-Shah
functional was been proposed. Many theoretical works as well as numerous
extensions have been studied rough out the years. This talk will focus on
introduction to these image segmentation functionals. I will start with
the review of Mumford-Shah functional and discuss Chan-Vese model. Some
new extensions will be presented at the end.

Wednesday, October 14, 2009 - 11:00 ,
Location: Skiles 269 ,
Bart Haegeman ,
INRIA, Montpellier, France ,
Organizer:

Hubbell's neutral model provides a rich theoretical framework to study
ecological communities. By coupling ecological and evolutionary time
scales, it allows investigating how communities are shaped by speciation
processes. The speciation model in the basic neutral model is particularly
simple, describing speciation as a point mutation event in a birth of a
single individual. The stationary species abundance distribution of the
basic model, which can be solved exactly, fits empirical data of
distributions of species abundances surprisingly well. More realistic
speciation models have been proposed such as the random fission model in
which new species appear by splitting up existing species. However, no
analytical solution is available for these models, impeding quantitative
comparison with data. Here we present a self-consistent approximation
method for the neutral community model with random fission speciation. We
derive explicit formulas for the stationary species abundance
distribution, which agree very well with simulations. However, fitting the
model to tropical tree data sets, we find that it performs worse than the
original neutral model with point mutation speciation.

Series: PDE Seminar

We study the asymptotic behavior of the infinite Darcy-Prandtl number Darcy-Brinkman-Boussinesq model for convection in porous media at small Brinkman-Darcy number. This is a singular limit involving a boundary layer with thickness proportional to the square root of the Brinkman-Darcynumber . This is a joint work with Jim Kelliher and Roger Temam.

Tuesday, October 13, 2009 - 15:00 ,
Location: Skiles 269 ,
Suzanne Lee ,
College of Management, Georgia Tech ,
Organizer: Christian Houdre

We propose a new two stage semi-parametric test and estimation procedure to
investigate predictability of stochastic jump arrivals in asset prices. It allows us
to search for conditional information that affects the likelihood of jump occurrences up
to the intra-day levels so that usual factor analysis for jump dynamics can be
achieved. Based on the new theory of inference, we find empirical evidence of jump clustering
in U.S. individual equity markets during normal trading hours. We also present other
intra-day jump predictors such as analysts recommendation updates and stock news
releases.

Series: Geometry Topology Seminar

The deformation variety is similar to the representation variety inthat it describes (generally incomplete) hyperbolic structures on3-manifolds with torus boundary components. However, the deformationvariety depends crucially on a triangulation of the manifold: theremay be entire components of the representation variety which can beobtained from the deformation variety with one triangulation but notanother, and it is unclear how to choose a "good" triangulation thatavoids these problems. I will describe the "extended deformationvariety", which deals with many situations that the deformationvariety cannot. In particular, given a manifold which admits someideal triangulation we can construct a triangulation such that we canrecover any irreducible representation (with some trivial exceptions)from the associated extended deformation variety.

Monday, October 12, 2009 - 13:00 ,
Location: Skiles 255 ,
Wei Zhu ,
University of Alabama (Department of Mathematics) ,
wzhu7@bama.ua.edu ,
Organizer: Sung Ha Kang

The Rudin-Osher-Fatemi (ROF) model is one of the most powerful and popular models in image denoising. Despite its simple form, the ROF functional has proved to be nontrivial to minimize by conventional methods. The difficulty is mainly due to the nonlinearity and poor conditioning of the related problem. In this talk, I will focus on the minimization of the ROF functional in the one-dimensional case. I will present a new algorithm that arrives at the minimizer of the ROF functional fast and exactly. The proposed algorithm will be compared with the standard and popular gradient projection method in accuracy, efficiency and other aspects.