Seminars and Colloquia by Series

Friday, October 23, 2009 - 15:00 , Location: Skiles 269 , Amey Kaloti , Georgia Tech , Organizer:

This is a 2 hour talk.

Abstract: Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with connections to contact topology. In these talks we will try to define the Heegaard Floer homology without assuming much background in low dimensional topology. One more goal is to present the combinatorial description for this theory.
Friday, October 23, 2009 - 14:00 , Location: Skiles 269 , Doug Hardin , Vanderbilt University , Organizer: Jeff Geronimo
I will review recent and classical results concerning the asymptotic properties (as N --> \infty) of 'ground state' configurations of N particles restricted to a d-dimensional compact set A\subset {\bf R}^p that minimize the Riesz s-energy functional \sum_{i\neq j}\frac{1}{|x_{i}-x_{j}|^{s}} for s>0. Specifically, we will discuss the following (1) For s < d, the ground state configurations have limit distribution as N --> \infty given by the equilibrium measure \mu_s, while the first order asymptotic growth of the energy of these configurations is given by the 'transfinite diameter' of A. (2) We study the behavior of \mu_s as s approaches the critical value d (for s\ge d, there is no equilibrium measure). In the case that A is a fractal, the notion of 'order two density' introduced by Bedford and Fisher naturally arises. This is joint work with M. Calef. (3) As s --> \infty, ground state configurations approach best-packing configurations on A. In work with S. Borodachov and E. Saff we show that such configurations are asymptotically uniformly distributed on A.
Thursday, October 22, 2009 - 15:00 , Location: Skiles 269 , Ton Dieker , (ISyE, Georgia Tech) , Organizer:
In this talk, we study an interacting particle system arising in the context of series Jackson queueing networks. Using effectively nothing more than the Cauchy-Binet identity, which is a standard tool in random-matrix theory, we show that its transition probabilities can be written as a signed sum of non-crossing probabilities. Thus, questions on time-dependent queueing behavior are translated to questions on non-crossing probabilities. To illustrate the use of this connection, we prove that the relaxation time (i.e., the reciprocal of the ’spectral gap’) of a positive recurrent system equals the relaxation time of a single M/M/1 queue with the same arrival and service rates as the network’s bottleneck station. This resolves a 1985 conjecture from Blanc on series Jackson networks. Joint work with Jon Warren, University of Warwick.
Thursday, October 22, 2009 - 12:05 , Location: Skiles 255 , Peter Whalen , Math, GT , Organizer: Robin Thomas
The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this talk I will present a combinatorial method of approaching the Jacobian of graphs by way of a chip-firing game played on its vertices. We then apply this chip-firing game to explicitly characterize the Jacobian of nearly complete graphs, those obtained from the complete graph by deleting either a cycle or two vertex-disjoint paths incident with all but one vertex. This is joint work with Sergey Norin.
Thursday, October 22, 2009 - 11:00 , Location: Skiles 269 , Jerry Bona , University of Illinois at Chicago , Organizer: Guillermo Goldsztein
After a brief account of some of the history of this classical subject, we indicate how such models are derived. Rigorous theory justifying the models will be discussed and the conversation will then turn to some applications. These will be drawn from questions arising in geophysics and coastal engineering, as time permits.
Series: Other Talks
Wednesday, October 21, 2009 - 14:00 , Location: Klaus, Room 1116 , Ravi Kannan , Microsoft Research Labs, Bangalore India , Organizer:

Tea and light refreshments 1:30 in Room 2222. Organizer: Santosh Vempala

Concentration results for the TSP, MWST and many other problems with random inputs show the answer is concentrated tightly around the mean. But most results assume uniform density of the input. We will generalize these to heavy-tailed inputs which seem to be ubiquitous in modern applications. To accomplish this, we prove two new general probability inequalities. The simpler first inequality weakens both hypotheses in Hoffding-Azuma inequality and is enough to tackle TSP, MWST and Random Projections. The second inequality further weakens the moment requirements and using it, we prove the best possible concentration for the long-studied bin packing problem as well as some others. Many other applications seem possible..
Wednesday, October 21, 2009 - 14:00 , Location: Skiles 269 , Yuliya Babenko , Sam Houston State University , Organizer:
In this talk we will discuss Kolmogorov and Landau type inequalities for the derivatives.  These are the inequalities which estimate the norm of the intermediate derivative of a function (defined on an interval, R_+, R, or their multivariate analogs) from some class in terms of the norm of the function itself and norm of its highest derivative. We shall present several new results on sharp inequalities of this type for special classes of functions (multiply monotone and absolutely monotone) and sequences. We will also highlight some of the techniques involved in the proofs (comparison theorems) and discuss several applications.
Series: Other Talks
Wednesday, October 21, 2009 - 13:00 , Location: Skiles 255 , Farbod Shokrieh , Ga Tech , Organizer: John Etnyre
As we have seen already, the global section functor is left exact.  To get a long exact sequence, I will first give the construction of derived functors in the more general setting of abelian categories withenough injectives. If time permits, I will then show that for any ringed space the category of all sheaves of Modules is an abelian category with enough injectives, and so we can construct sheaf cohomology as the right derived functors of the global section functor. The relation with Cech cohomology will be studied in a subsequent talk.
Wednesday, October 21, 2009 - 12:00 , Location: Skiles 171 , Doron Lubinsky , School of Mathematics, Georgia Tech , , Organizer:
Orthogonal polynomials are an important tool in many areas of pure and applied mathematics. We outline one application in random matrix theory. We discuss generalizations of orthogonal polynomials such as the Muntz orthogonal polynomials investigated by Ulfar Stefansson. Finally, we present some conjectures about biorthogonal polynomials, which would be a great Ph.D. project for any interested student.
Wednesday, October 21, 2009 - 11:00 , Location: Skiles 269 , Klas Udekwu , Biology, Emory University , , Organizer:
Treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Surprisingly, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge and the dose and term of antibiotic treatment has long been determined by clinicians empirically and intuitively. There is a recent drive to theoretically and experimentally rationalize antibiotic treatment protocols with the aim to them and to design protocols which maximize antibiotics’ efficacy while preventing resistance emergence. Central to these endeavors are the pharmacodynamics of the antibiotic(s) and bacteria, PD (the relationship between the concentration of the antibiotic and the rate of growth/death of bacteria), and the pharmacokinetics of the antibiotic, PK (the distribution and change in concentration of the antibiotics in a treated host) of each bacteria.  The procedures for estimating of PD and PK parameters are well established and standardized worldwide.  Although different PK parameters are commonly employed for the design of antibiotic treatment protocols most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). The Clinical and Laboratory Standards Institute (CLSI) approved method for estimating MICs defines testing conditions that are optimal for the antibiotic, like low densities and exponential growth, rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts.   Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating, and these bacteria are rarely planktonic, rather residing as colonies or within matrices called biofilms which sometimes include other species of bacteria.  Refractoriness (non-inherited resistance) is the term used to describe an observed inefficacy of antibiotics on otherwise antibiotic-susceptible bacterial populations. This talk will focus on our efforts to describe the pharmacodynamic relationship between Staphylococcus aureus and antibiotics of six classes in the light of antibiotic refractoriness.  I will begin by addressing the effects of cell density on the MIC index, after which I intend to present unpublished data descriptive of physiology-related effects on antibiotic efficacy.  Additionally, we will explore the potential contribution of such in vitro results, to observed/predicted clinical outcomes using standard mathematical models of antibiotic treatment which also serve to generate testable hypotheses.