Seminars and Colloquia by Series

The entropy production problem and Villani's conjecture

Series
SIAM Student Seminar
Time
Friday, October 8, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Amit EinavSchool of Mathematics, Georgia Tech
In 1956 Mark Kac published his paper about the Foundation of Kinetic Theory in which he gave a mathematical, probabilistic description of a system of N particles colliding randomly. An interesting result that was found, though not causing any surprise, was the convergence to the stable equilibrium state. The question of the rate of the L2 convergence interested Kac and he conjectured that the spectral gap governing the convergence is uniformly bounded form below as N goes to infinity. While this was proved to be true, and even computed exactly, many situations show that the time scale of the convergence for very natural cases is proportional to N, while we would hope for an exponential decay. A different approach was considered, dealing with a more natural quantity, the entropy. In recent paper some advancement were made about evaluating the rate of change, and in 2003 Villani conjectured that the corresponding 'spectral gap', called the entropy production, is of order of 1/N. In our lecture we'll review the above topics and briefly discuss recently found results showing that the conjecture is essentially true.

Small Noise: Dynamical Systems and Probability put together

Series
SIAM Student Seminar
Time
Friday, September 24, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Serjio AlmandaSchool of Mathematics, Georgia Tech
In this talk I will outline a topic that has been of interest due to its applicability in physics and engineering. The so called small noise model is a very technical subject that lies in the center of probability theory and usually study thorough a large deviations approach. I will explain this terminology and why is the correlation with dynamical systems so strong. Recent developments will be given at the end if time allows.

A brief introduction to copulas and related problems

Series
SIAM Student Seminar
Time
Friday, April 2, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ruodu WangSchool of Mathematics, Georgia Tech
A copula C of n arbitrary random variables X_1, ..., X_n contains all the information about their dependence. First I will briefly introduce the definition, basic properties and elementary examples of copulas, as well as Sklar's Theorem (1959). Then I will present a family of multivariate copulas whose marginal copula belongs to a family of extreme copulas. Finally I will discuss a minimization problem related to copula, which is still open. The talk should be easy to understand for all level audience who have knowledge of basic probability theory

Sparsity in machine learning: recovery in convex hulls of infinite dictionaries

Series
SIAM Student Seminar
Time
Friday, March 12, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Stanislav MinskerSchool of Mathematics, Georgia Tech
We will start with a brief introduction to the broad area of machine learning, with the focus on empirical risk minimization methods and their connection to the theory of empirical processes. Using some results from our recent work with V. Koltchinskii, I will explain how sparsity affects the risk bounds.

The geometry of dissipative evolution equation

Series
SIAM Student Seminar
Time
Friday, March 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao LiGeorgia Tech
Last semester, I reviewed the relation between dynamical system, Fokker-Planck equation and thermodynamics (free energy and Gibbs distribution). This time let's go further. I will review the geometric properties of a kind of dissipative evolution equations. I will explain why this kind of evolutionary equations (Fokker-Planck equation, nonlinear Fokker-Planck equation, Porous medium equation) are the gradient flow of some energy function on a Riemannian manifold -- 2-Wasserstein metric space.

A Survey of Hardy Inequalities and their Optimization

Series
SIAM Student Seminar
Time
Friday, February 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Craig A. SloaneSchool of Mathematics, Georgia Tech
This will be an introductory talk about Hardy inequalities. These inequalities are solutions to optimization problems, and their results are well-known. I will survey these results, and discuss some of the techniques used to solve these problems. The applications of Hardy inequalities are broad, from PDE's and mathematical physics to brownian motion. This talk will also serve as a lead-in to my talk at the Analysis seminar next Wednesday in which I discuss some current results that Michael Loss and I have obtained.

Introduction to the Latex

Series
SIAM Student Seminar
Time
Friday, February 12, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 156 (undergraduate computer lab)
Speaker
Mitch KellerSchool of Mathematics, Georgia Tech
This is an introductory talk to everyone who wants to learn skills in Latex. We will discuss including and positioning graphics and the beamer document class for presentations. A list of other interesting topics will be covered if time permits.

The existence and uniqueness of one minimization problem

Series
SIAM Student Seminar
Time
Friday, February 5, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Linwei XinSchool of Mathematics, Georgia Tech
We are dealing with the following minimization problem: inf {I(\mu): \mu is a probability measure on R and \int f(x)=t_{0}}, where I(\mu) = \int (x^2)/2 \mu(dx) + \int\int log|x-y|^{-1} \mu(dx)\mu(dy), f(x) is a bounded continuous function and t is a given real number. Its motivation and its connection to radom matrices theory will be introduced. We will show that the solution is unique and has a compact support. The possible extension of the class of f(x) will be discussed.

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