Seminars and Colloquia by Series

Pebbling graphs of diameter four

Series
Graph Theory Seminar
Time
Thursday, November 20, 2008 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Carl Yerger – School of Mathematics, Georgia Tech
Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one of these on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that given any configuration of k pebbles on G and any specified vertex v in V(G), there is a sequence of pebbling moves that sends a pebble to v. We will show that the pebbling number of a graph of diameter four on n vertices is at most 3n/2 + O(1), and this bound is best possible up to an additive constant. This proof, based on a discharging argument and a decomposition of the graph into ''irreducible branches'', generalizes work of Bukh on graphs of diameter three. Further, we prove that the pebbling number of a graph on n vertices with diameter d is at most (2^{d/2} - 1)n + O(1). This also improves a bound of Bukh.

Geometric Discrepancy and Harmonic Analysis

Series
Analysis Seminar
Time
Thursday, November 20, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Dmitriy Bilyk – IAS & U South Carolina

Please Note: Note change in time.

The theory of geometric discrepancy studies different variations of the following question: how well can one approximate a uniform distribution by a discrete one, and what are the limitations that necessarily arise in such approximations. Historically, the methods of harmonic analysis (Fourier transform, Fourier series, wavelets, Riesz products etc) have played a pivotal role in the subject. I will give an overview of the problems, methods, and results in the field and discuss some latest developments.

Some game theoretic issues in Nash bargaining

Series
ACO Student Seminar
Time
Wednesday, November 19, 2008 - 13:30 for 2 hours
Location
ISyE Executive Classroom
Speaker
Lei Wang – ACO Student, School of Mathematics, Georgia Tech
Nash bargaining was first modeled in John Nash's seminal 1950 paper. In his paper, he used a covex program to give the Nash bargaining solution, which satifies many nature properties. Recently, V.Vazirani defined a class of Nash bargaining problem as Uniform Nash Bargaining(UNB) and also defined a subclass called Submodular Nash Bargaining (SNB). In this talk, we will consider some game theoretic issues of UNB: (1) price of bargaining; (2) fully competitiveness; (3) min-max and max-min fairness and we show that each of these properties characterizes the subclass SNB.

Flapping and Swimming Motions in Fluids

Series
Research Horizons Seminar
Time
Wednesday, November 19, 2008 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Silas Alben – School of Mathematics, Georgia Tech
We examine some problems in the coupled motions of fluids and flexible solid bodies. We first present some basic equations in fluid dynamics and solid mechanics, and then show some recent asymptotic results and numerical simulations. No prior experience with fluid dynamics is necessary.

On Shock-Free Periodic Solutions for the Euler Equations

Series
PDE Seminar
Time
Tuesday, November 18, 2008 - 15:15 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Robin Young – University of Massachusetts, Amherst
We consider the existence of periodic solutions to the Euler equations of gas dynamics. Such solutions have long been thought not to exist due to shock formation, and this is confirmed by the celebrated Glimm-Lax decay theory for 2x2 systems. However, in the full 3x3 system, multiple interaction effects can combine to slow down and prevent shock formation. In this talk I shall describe the physical mechanism supporting periodicity, describe combinatorics of simple wave interactions, and develop periodic solutions to a "linearized" problem. These linearized solutions have a beautiful structure and exhibit several surprising and fascinating phenomena. I shall also discuss partial progress on the perturbation problem: this leads us to problems of small divisors and KAM theory. This is joint work with Blake Temple.

The dynamics of two classes of singular traveling wave systems

Series
CDSNS Colloquium
Time
Monday, November 17, 2008 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Jibin Li – Kunming Univeristy of Science and Technology and Zhejiang Normal University
Nonlinear wave phenomena are of great importance in the physical world and have been for a long time a challenging topic of research for both pure and applied mathematicians. There are numerous nonlinear evolution equations for which we need to analyze the properties of the solutions for time evolution of the system. As the first step, we should understand the dynamics of their traveling wave solutions. There exists an enormous literature on the study of nonlinear wave equations, in which exact explicit solitary wave, kink wave, periodic wave solutions and their dynamical stabilities are discussed. To find exact traveling wave solutions for a given nonlinear wave system, a lot of methods have been developed. What is the dynamical behavior of these exact traveling wave solutions? How do the travelling wave solutions depend on the parameters of the system? What is the reason of the smoothness change of traveling wave solutions? How to understand the dynamics of the so-called compacton and peakon solutions? These are very interesting and important problems. The aim of this talk is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions and understand their dynamics for two classes of singular nonlinear traveling systems.

Lower bounds for the Hilbert number of polynomial systems

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 17, 2008 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Maoan Han – Shanghai Normal University
Let H(m) denote the maximal number of limit cycles of polynomial systems of degree m. It is called the Hilbert number. The main part of Hilbert's 16th problem posed in 1902 is to find its value. The problem is still open even for m=2. However, there have been many interesting results on the lower bound of it for m\geq 2. In this paper, we give some new lower bounds of this number. The results obtained in this paper improve all existing results for all m\geq 7 based on some known results for m=3,4,5,6. In particular, we confirm the conjecture H(2k+1) \geq (2k+1)^2-1 and obtain that H(m) grows at least as rapidly as \frac{1}{2\ln2}(m+2)^2\ln(m+2) for all large m.

Hyperbolic volume and torsions of 3-manifolds

Series
Geometry Topology Working Seminar
Time
Friday, November 14, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Thang Le – School of Mathematics, Georgia Tech
We will explain the famous result of Luck and Schick which says that for a large class of 3-manifolds, including all knot complements, the hyperbolic volume is equal to the l^2-torsion. Then we speculate about the growth of homology torsions of finite covers of knot complements. The talk will be elementary and should be accessible to those interested in geometry/topology.

Computing Junction Forests from Filtrations of Simplicial Complexes

Series
Stochastics Seminar
Time
Friday, November 14, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Sayan Mukherjee – Department of Statistical Science, Duke University
Let X=(X_1,\ldots,X_n) be a n-dimensional random vector for which the distribution has Markov structure corresponding to a junction forest, assuming functional forms for the marginal distributions associated with the cliques of the underlying graph. We propose a latent variable approach based on computing junction forests from filtrations. This methodology establishes connections between efficient algorithms from Computational Topology and Graphical Models, which lead to parametrizations for the space of decomposable graphs so that: i) the dimension grows linearly with respect to n, ii) they are convenient for MCMC sampling.

Reflections on a favorite child

Series
ACO Distinguished Lecture
Time
Thursday, November 13, 2008 - 16:30 for 2 hours
Location
Klaus 1116
Speaker
Harold W. Kuhn – Princeton University

Please Note: RECEPTION TO FOLLOW

Fifty five years ago, two results of the Hungarian mathematicians, Koenig and Egervary, were combined using the duality theory of linear programming to construct the Hungarian Method for the Assignment Problem. In a recent reexamination of the geometric interpretation of the algorithm (proposed by Schmid in 1978) as a steepest descent method, several variations on the algorithm have been uncovered, which seem to deserve further study. The lecture will be self-contained, assuming little beyond the duality theory of linear programming. The Hungarian Method will be explained at an elementary level and will be illustrated by several examples. We shall conclude with account of a posthumous paper of Jacobi containing an algorithm developed by him prior to 1851 that is essentially identical to the Hungarian Method, thus anticipating the results of Koenig (1931), Egervary (1931), and Kuhn (1955) by many decades.

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