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.
[Special day and location] Scaling properties and suppression of Fermi acceleration in time dependent billiardsWednesday, 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) , email@example.com , 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.
Series: Combinatorics Seminar
In this talk I will discuss a new technique discovered by myself and Olof Sisask which produces many new insights in additive combinatorics, not to mention new proofs of classical theorems previously proved only using harmonic analysis. Among these new proofs is one for Roth's theorem on three-term arithmetic progressions, which gives the best bounds so far achieved by any combinatorial method. And another is a new proof that positive density subsets of the integers mod p contain very long arithmetic progressions, first proved by Bourgain, and improved upon by Ben Green and Tom Sanders. If time permits, I will discuss how the method can be applied to the 2D corners problem.