Seminars and Colloquia by Series

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 Wang – School 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 Minsker – School 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 Li – Georgia 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. Sloane – School 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 Keller – School 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 Xin – School 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.

The limit distribution the longest significance path(LSP) in point cloud

Series
SIAM Student Seminar
Time
Friday, January 29, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Kai Ni – School of Mathematics, Georgia Tech
In 2006, my coadvisor Xiaoming Huo and his colleague published an annal of statistics paper which designs an asymptotically powerful testing algorithm to detect the potential curvilinear structure in a messy point cloud image. However, such an algorithm involves a membership threshold and a decision threshold which are not well defined in that paper because the distribution of LSP was unknown. Later on, Xiaoming's student Chen, Jihong found some connections between the distribution of LSP and the so-called Erdos-Renyi law. In some sense, the distribution of LSP is just a generalization of the Erdos-Renyi law. However this JASA paper of Chen, Jihong had some restrictions and only partially found out the distribution of LSP. In this talk, I will show the result of the JASA paper is actually very close to the distribution of LSP. However, these is still much potential work to do in order to strengthen this algorithm.

Reducing the Size of a Matrix While Maintaining its Spectrum

Series
SIAM Student Seminar
Time
Friday, January 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Benjamin Webb – School of Mathematics, Georgia Tech
The Fundamental Theorem of Algebra implies that a complex valued nxn matrix has n eigenvalues (including multiplicities). In this talk we introduce a general method for reducing the size of a square matrix while preserving this spectrum. This can then be used to improve on the classic eigenvalue estimates of Gershgorin, Brauer, and Brualdi. As this process has a natural graph theoretic interpretation this talk should be accessible to most anyone with a basic understanding of matrices and graphs. These results are based on joint work with Dr. Bunimovich.

Simulation Study of the Length of Longest Increasing Subsequence of Finite Alphabets

Series
SIAM Student Seminar
Time
Friday, November 20, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Huy Huynh – Georgia Tech
Let X_1, X_2,...,X_n be a sequence of i.i.d random variables with values in a finite alphabet {1,...,m}. Let LI_n be the length of the longest increasing subsequence of X_1,...,X_n. We shall express the limiting distribution of LI_n as functionals of m and (m-1)- dimensional Brownian motions as well as the largest eigenvalue of Gaussian Unitary Ensemble (GUE) matrix. Then I shall illustrate simulation study of these results

From Gibbs free energy to the dynamical system with random perturbation

Series
SIAM Student Seminar
Time
Friday, November 13, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yao Li – School of Mathematics, Georgia Tech
Gibbs free energy plays an important role in thermodynamics and has strong connection with PDE, Dynamical system. The results about Gibbsfree energy in 2-Wasserstein metric space are known recently.First I will introduce some basic things, so the background knowledge isnot required. I will begin from the classic definition of Gibbs freeenergy functional and then move to the connection between Gibbs freeenergy and the Fokker-Planck equation, random perturbation of gradientsystems. Second, I will go reversely: from a dynamical system to thegeneralized Gibbs free energy functional. I will also talk about animportant property of the Gibbs free energy functional: TheFokker-Planck equation is the gradient flux of Gibbs free energyfunctional in 2-Wasserstein metric.So it is natural to consider a question: In topological dynamical systemand lattice dynamical system, could we give the similar definition ofGibbs free energy, Fokker-Planck equation and so on? If time allowed, Iwill basicly introduce some of my results in these topics.

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