Seminars and Colloquia by Series

Inequalities for Derivatives and their Applications

Series
Analysis Seminar
Time
Wednesday, October 21, 2009 - 14:00 for 8 hours (full day)
Location
Skiles 269
Speaker
Yuliya BabenkoSam Houston State University
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.

ARC-ACO Colloquium - Concentration under Heavy Tails

Series
Other Talks
Time
Wednesday, October 21, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus, Room 1116
Speaker
Ravi KannanMicrosoft Research Labs, Bangalore India

Please Note: 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..

The Grothendieck definition of sheaf cohomology

Series
Other Talks
Time
Wednesday, October 21, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Farbod ShokriehGa Tech
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.

Title: Orthogonal and Biorthogonal Polyonmials

Series
Research Horizons Seminar
Time
Wednesday, October 21, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Doron LubinskySchool of Mathematics, Georgia Tech
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.

Antibiotics: Efficacy 'measures' and physiological state effects

Series
Mathematical Biology Seminar
Time
Wednesday, October 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Klas UdekwuBiology, Emory University
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.

Boundary Value Problems for Nonlinear Dispersive Wave Equations

Series
PDE Seminar
Time
Tuesday, October 20, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Hongqiu ChenUniversity of Memphis
Under the classical small-amplitude, long wave-length assumptions in which the Stokes number is of order one, so featuring a balance between nonlinear and dispersive effects, the KdV-equation u_t+ u_x + uu_x + u_xxx = 0 (1) and the regularized long wave equation, or BBM-equation u_t + u_x + uu_x-u_xxt = 0 (2) are formal reductions of the full, two-dimensional Euler equations for free surface flow. This talk is concerned with the two-point boundary value problem for (1) and (2) wherein the wave motion is specified at both ends of a finite stretch of length L of the media of propagation. After ascertaining natural boundary specifications that constitute well posed problems, it is shown that the solution of the two-point boundary value problem, posed on the interval [0;L], say, converges as L converges to infinity, to the solution of the quarter-plane boundary value problem in which a semi-infinite stretch [0;1) of the medium is disturbed at its finite end (the so-called wavemaker problem). In addition to its intrinsic interest, our results provide justification for the use of the two-point boundary-value problem in numerical studies of the quarter plane problem for both the KdV-equation and the BBM-equation.

Modeling the forward surface of mortality

Series
Mathematical Finance/Financial Engineering Seminar
Time
Tuesday, October 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Daniel BauerGeorgia State University
In recent literature, different mothods have been proposed on how to define and model stochastic mortality. In most of these approaches, the so-called spot force of mortality is modeled as a stochastic process. In contrast to such spot force models, forward force mortality models infer dynamics on the entire age/term-structure of mortality. This paper considers forward models defined based on best-estimate forecasts of survival probabilities as can be found in so-called best-estimate generation life tables. We provide a detailed analysis of forward mortality models deriven by finite-dimensional Brownian motion. In particular, we address the relationship to other modeling approaches, the consistency problem of parametric forward models, and the existence of finite dimensional realizations for Gaussian forward models. All results are illustrated based on a simple example with an affine specification.

Sylvester's Four Point Constant: closing in (or are we?)

Series
Graph Theory Seminar
Time
Tuesday, October 20, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Gelasio SalazarUniversidad Autonoma de San Luis Potosi
In 1865, Sylvester posed the following problem: For a region R in the plane,let q(R) denote the probability that four points chosen at random from Rform a convex quadrilateral. What is the infimum q* of q(R) taken over allregions R? The number q* is known as Sylvester's Four Point Problem Constant(Sylvester's Constant for short). At first sight, it is hard to imagine howto find reasonable estimates for q*. Fortunately, Scheinerman and Wilf foundthat Sylvester's Constant is intimately related to another fundamentalconstant in discrete geometry. The rectilinear crossing number of rcr(K_n)the complete graph K_n is the minimum number of crossings of edges in adrawing of K_n in the plane in which every edge is a straight segment. Itis not difficult to show that the limit as n goes to infinity ofrcr(K_n)/{n\choose 4} exists; this is the rectilinear crossing numberconstant RCR. Scheinerman and Wilf proved a surprising connection betweenthese constants: q* = RCR. Finding estimates of rcr(K_n) seems like a moreapproachable task. A major breakthrough was achieved in 2003 by Lovasz,Vesztergombi, Wagner, and Welzl, and simultaneously by Abrego andFernandez-Merchant, who unveiled an intimate connection of rcr(K_n) withanother classical problem of discrete geometry, namely the number of

Interpolation in Bergman Spaces

Series
Analysis Working Seminar
Time
Monday, October 19, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Brett WickGeorgia Tech
In this working seminar we will give a proof of Seip's characterization of interpolating sequences in the Bergman space of analytic functions. This topic has connection with complex analysis, harmonic analysis, and time frequency analysis and so hopefully many of the participants would be able to get something out of the seminar. The initial plan will be to work through his 1993 Inventiones Paper and supplement this with material from his book "Interpolation and Sampling in Spaces of Analytic Functions". Notes will be generated as the seminar progresses.

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