## Seminars and Colloquia by Series

### Couple of variational models for multi-phase segmentation

Series
PDE Seminar
Time
Tuesday, January 27, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
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. In this talk, I will focus on couple of variational models for multi-phase segmentation. For the first model, we propose a model built upon the phase transition model of Modica and Mortola in material sciences and a properly synchronized fitting term that complements it. For the second model, we propose a variational functional for an unsupervised multiphase segmentation, by adding scale information of each phase. This model is able to deal with the instability issue associated with choosing the number of phases for multiphase segmentation.

### A global analysis of a multistrain viral model with mutations

Series
CDSNS Colloquium
Time
Monday, January 26, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Sergei PilyuginUniversity of Florida
I will present a generalization of a classical within-host model of a viral infection that includes multiple strains of the virus. The strains are allowed to mutate into each other. In the absence of mutations, the fittest strain drives all other strains to extinction. Treating mutations as a small perturbation, I will present a global stability result of the perturbed equilibrium. Whether a particular strain survives is determined by the connectivity of the graph describing all possible mutations.

### Sparse Solutions of Underdetermined Linear Systems

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 26, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ming-Jun LaiUniversity of Georgia
I will first explain why we want to find the sparse solutions of underdetermined linear systems. Then I will explain how to solve the systems using \ell_1, OGA, and \ell_q approaches. There are some sufficient conditions to ensure that these solutions are the sparse one, e.g., some conditions based on restricted isometry property (RIP) by Candes, Romberg, and Tao'06 and Candes'08. These conditions are improved recently in Foucart and Lai'08. Furthermore, usually, Gaussian random matrices satisfy the RIP. I shall explain random matrices with strictly sub-Gaussian random variables also satisfy the RIP.

### Introduction to the h-principle

Series
Other Talks
Time
Friday, January 23, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Mohammad GhomiSchool of Mathematics, Georgia Tech
h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

### Elliptic curves and chip-firing games on wheel graphs

Series
Combinatorics Seminar
Time
Friday, January 23, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Gregg MusikerMIT
In this talk, I will discuss chip-firing games on graphs, and the related Jacobian groups. Additionally, I will describe elliptic curves over finite fields, and how such objects also have group structures. For a family of graphs obtained by deforming the sequence of wheel graphs, the cardinalities of the Jacobian groups satisfy a nice reciprocal relationship with the orders of elliptic curves as we consider field extensions. I will finish by discussing other surprising ways that these group structures are analogous. Some of this research was completed as part of my dissertation work at the University of California, San Diego under Adriano Garsia's guidance.

### Introduction to the h-principle

Series
Geometry Topology Working Seminar
Time
Friday, January 23, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
$h$-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the $C^1$ isometric embedding theorem of Nash.

### Some interesting examples in the conditional expectation and martingale

Series
SIAM Student Seminar
Time
Friday, January 23, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Linwei XinSchool of Mathematics, Georgia Tech
In this talk, I will focus on some interesting examples in the conditional expectation and martingale, for example, gambling system "Martingale", Polya's urn scheme, Galton-Watson process, Wright-Fisher model of population genetics. I will skip the theorems and properties. Definitions to support the examples will be introduced. The talk will not assume a lot of probability, just some basic measure theory.

### Global asymptotic analysis of the Painleve transcendents. The Riemann-Hilbert Approach

Series
School of Mathematics Colloquium
Time
Thursday, January 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alexander ItsIndiana University-Purdue University Indianapolis
In this talk we will review some of the global asymptotic results obtained during the last two decades in the theory of the classical Painleve equations with the help of the Isomonodromy - Riemann-Hilbert method. The results include the explicit derivation of the asymptotic connection formulae, the explicit description of linear and nonlinear Stokes phenomenon and the explicit evaluation of the distribution of poles. We will also discuss some of the most recent results emerging due to the appearance of Painleve equations in random matrix theory. The Riemann-Hilbert method will be outlined as well.

### A Survey of Results for Deletion Channels and Related Synchronization Channels

Series
ACO Colloquium
Time
Wednesday, January 21, 2009 - 16:30 for 2 hours
Location
Klaus
Speaker
Michael MitzenmacherHarvard University
We describe recent progress in the study of the binary deletion channel and related channels with synchronization errors, including a clear description of many open problems in this area. As an example, while the capacity of the binary symmetric error channel and the binary erasure channel have been known since Shannon, we still do not have a closed-form description of the capacity of the binary deletion channel. We highlight a recent result that shows that the capacity is at least (1-p)/9 when each bit is deleted independently with fixed probability p.