Seminars and Colloquia by Series

Introduction of variational approaches to image segmentation.

Series
Research Horizons Seminar
Time
Wednesday, October 14, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Sung Ha KangSchool of Mathematics, Georgia Tech
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.

The neutral community model with random fission speciation

Series
Mathematical Biology Seminar
Time
Wednesday, October 14, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Bart HaegemanINRIA, Montpellier, France
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.

Boundary layer associated with the Darcy-Brinkman-Boussinesq system

Series
PDE Seminar
Time
Tuesday, October 13, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Xiaoming WangFlorida State University
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.

Jumps and Information Flow in Financial Markets

Series
Mathematical Finance/Financial Engineering Seminar
Time
Tuesday, October 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Suzanne LeeCollege of Management, Georgia Tech
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.

A generalisation of the deformation variety

Series
Geometry Topology Seminar
Time
Monday, October 12, 2009 - 14:05 for 2 hours
Location
Skiles 269
Speaker
Henry SegermanUTexas Austin
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.

A fast and exact algorithm of minimizing the Rudin-Osher-Fatemi functional in one dimension

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 12, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Wei ZhuUniversity of Alabama (Department of Mathematics)
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.

A new probabilistic/combinatorial method in additive combinatorics

Series
Combinatorics Seminar
Time
Friday, October 9, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ernie CrootSchool of Math, Georgia Tech
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.

On classification of of high-dimensional manifolds-II

Series
Geometry Topology Working Seminar
Time
Friday, October 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Igor BelegradekGeorgia Tech
This 2 hour talk is a gentle introduction to simply-connected sugery theory (following classical work by Browder, Novikov, and Wall). The emphasis will be on classification of high-dimensional manifolds and understanding concrete examples.

Nonuniqueness for some stochastic partial differential equations

Series
Stochastics Seminar
Time
Friday, October 9, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 154 (Unusual time and room)
Speaker
Carl MuellerUniversity of Rochester
One of the most important stochastic partial differential equations, known as the superprocess, arises as a limit in population dynamics. There are several notions of uniqueness, but for many years only weak uniqueness was known. For a certain range of parameters, Mytnik and Perkins recently proved strong uniqueness. I will describe joint work with Barlow, Mytnik and Perkins which proves nonuniqueness for the parameters not included in Mytnik and Perkins' result. This completely settles the question for strong uniqueness, but I will end by giving some problems which are still open.

Approximations of Short Term Options Pricing Under Stochastic Volatility Models with Jumps

Series
SIAM Student Seminar
Time
Friday, October 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Allen HoffmeyerSchool of Mathematics, Georgia Tech
This talk is based on a paper by Medvedev and Scaillet which derives closed form asymptotic expansions for option implied volatilities (and option prices). The model is a two-factor jump-diffusion stochastic volatility one with short time to maturity. The authors derive a power series expansion (in log-moneyness and time to maturity) for the implied volatility of near-the-money options with small time to maturity. In this talk, I will discuss their techniques and results.

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