Seminars and Colloquia Schedule

Tropical and Berkovich analytic curves

Series
Tropical Geometry Seminar
Time
Wednesday, October 20, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Matt Baker – Georgia Tech
We will discuss the relationship between a Berkovich analytic curve over a complete and algebraically closed non-Archimedean field and its tropicalizations, paying special attention to the natural metric structure on both sides. This is joint work with Sam Payne and Joe Rabinoff.

Orthogonal Polynomials and Beyond

Series
Research Horizons Seminar
Time
Wednesday, October 20, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Lilian Wong – School of Mathematics - Georgia Institute of Technology

Hosts: Yao Li and Ricardo Restrepo

This will be an expository talk on the study of orthogonal polynomials on the real line and on the unit circle. Topics include recurrence relations, recurrence coefficients and simple examples. The talk will conclude with applications of orthogonal polynomials to other areas of research.

Polya sequences, gap theorems, and Toeplitz kernels

Series
Analysis Seminar
Time
Wednesday, October 20, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mishko Mitkovski – Georgia Tech
A separated sequence of real numbers is called a Polya sequence if the only entire functions of zero type which are bounded on this sequence are the constants. The Polya-Levinson problem asks for a description of all Polya sequences. In this talk, I will present some points of the recently obtained solution. The approach is based on the use of Toeplitz operators and de Branges spaces of entire functions. I will also present some partial results about the related Beurling gap problem.

The Graph Removal Lemma

Series
Combinatorics Seminar
Time
Wednesday, October 20, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jacob Fox – Math, MIT
Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n^h) copies of H can be made H-free by removing o(n^2) edges. We give a new proof which avoids Szemeredi’s regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers questions of Alon and Gowers.

Public Lecture - Celebration of Mind - The Mathematics, Magic & Mystery of Martin Gardner

Series
Other Talks
Time
Thursday, October 21, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Klaus 1456
Speaker
Colm Mulcahy – Spelman College
Martin Gardner (1914-2010) "brought more mathematics to more millions than anyone else,"  according to Elwyn R. Berlekamp, John H. Conway & Richard K. Guy. Who was this man, how was he so influential, and will his legacy matter in the 22nd century? We'll try to answer these questions.This event is part of a one-day global celebration of the life of Martin Gardner. See www.g4g-com.org for information on Atlanta's Celebration of Mind party.

Asymptotic properties of random matrices of long-range percolation model

Series
Stochastics Seminar
Time
Thursday, October 21, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Slim Ayadi – School of Math, Georgia Tech
We study the spectral properties of matrices of long-range percolation model. These are N*N random real symmetric matrices H whose elements are independent random variables taking zero value with probability 1-\psi((i-j)/b), b\in \R^{+}, where \psi is an even positive function with \psi(t)<1 and vanishing at infinity. We show that under rather general conditions on the probability distribution of H(i,j) the semicircle law is valid for the ensemble we study in the limit N,b\to\infty. In the second part, we study the leading term of the correlation function of the resolvent G(z)=(H-z)^{-1} with large enough |Imz| in the limit N,b\to\infty, b=O(N^{\alpha}), 1/3<\alpha<1. We show that this leading term, when considered in the local spectral scale leads to an expression found earlier by other authors for band random matrix ensembles. This shows that the ensemble we study and that of band random matrices belong to the same class of spectral universality.

On nonparametric multivariate statistical process control charts

Series
SIAM Student Seminar
Time
Friday, October 22, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Giang Do – School of Mathematics, Georgia Tech
Statistical Process Control Charts are key tools in monitoring and controlling production processes to achieve conforming, high quality products. We will conduct a literature review on the Nonparametric Multivariate Statistical Process Control Charts to see what has been done in the area and how the methods have been applied.

Small-time Expansions of the Distributions, Densities, and option prices of stochastic volatility models with Levy jumps

Series
Mathematical Finance/Financial Engineering Seminar
Time
Friday, October 22, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Ruoting Gong – School of Mathematics, Georgia Tech

Hosted by Christian Houdre and Liang Peng.

We consider a stochastic volatility model with Levy jumps for a log-return process Z = (Z_t )_{t\ge 0}of the form Z = U + X , where U = (U_t)_{t\ge 0}is a classical stochastic volatility model and X = (X_t)_{t\ge 0} is an independent Levy process with absolutely continuous Levy measure \nu. Small-time expansion, of arbitrary polynomial order in time t, are obtained for the tails P(Z_t\ge z), z > 0 , and for the call-option prices E( e^{z+ Z_t| - 1), z \ne 0, assuming smoothness conditions on the Levy density away from the origin and a small-time large deviation principle on U. The asymptotic behavior of the corresponding implied volatility is also given. Our approach allows for a unified treatment of general payoff functions of the form \phi(x)1_{x\ge z} for smooth function \phi and z > 0. As a consequence of our tail expansions, the polynomial expansions in t of the transition densities f_t are obtained under rather mild conditions.

Dependent Random Choice

Series
ACO Seminar
Time
Friday, October 22, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jacob Fox – Mathematics, MIT
We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique has had several striking applications to Extremal Graph Theory, Ramsey Theory, Additive Combinatorics, and Combinatorial Geometry. In this talk, which is based on a survey with Benny Sudakov, we discuss some of these applications.