1. Friday, February 13, 2004. Time: TBA. Room: MP 3314.
Speaker: Professor Jeffrey Geronimo, Georgia Institute of Technology, Visiting Lecture Series
Title: On a two variable extension of the Fejer- Riesz lemma
Abstract: In 1915 Fejer and Riesz showed that every
positive trigonometric polynomial can factor as a magnitude squared of a
polynomial of the same degree. The speaker recalled the lemma and presented a
two variable extension.
2.
Friday February 20, 2004, Time: TBA. Room: MP 3314. Visiting lecture,
Professor J. M. Landsberg, School of Mathematics, Georgia Institute of
Mathematics.
3. Title.Secant Varieties, Matrix multiplication and Baysean networks .
Abstract.The speaker will described a geometric object, Secant varieties of Segre varieties and then describe its use in Computer Science and Mathematical Biology.
4. Friday, February 27, 2004. Time: TBA. Room: MP 3314.
Speaker: Dr. John Hawkins
Title: Galerkins Method for Nonlinear Boundary Value Problems
Abstract: The basis for the talk is his own Dissertation under the same
title. The Nonlinear boundary Value problem is converted to a related problem
with homogeneous boundary conditions and an extention of Galerkins Method to the
Nonlinear Boundary Value Problem is investigated to obtain approximate solutions
to the related Boundary value problem.The approximate solution to the original
problem is obtained from approximate solution to the related problem.
Assumptions and basic results will be discussed.
5. Friday, March 5, 2004. Time: TBA. Room: MP 3314.
Speaker: Prof. Francis Jordan
Title: Continua for which local connectivity of functions gives global connectivity.
Abstract: In 1959 John Stallings asked for conditions which force local connectivity functions to be connectivity functions.This is a standard topological problem involving gluing well behaved pieces of an object together to show that object is well behaved globally. A fairly general answer to Stallings question is given by showing that local connectivity functions and connectivity functions are indistinguishable for connected locally connected compact metric spaces.
6. Friday, March 12, 2004. Time: TBA. Room: MP 3314.
Speaker: Prof. Matthew Schuette
Title: A look at two endemic infectious disease models with quarantine
Abstract: In this talk the author will discuss two models from the paper.
Effects of quarantine in six endemic models
for infectious disease by
Hethcote, Zhien and Shengbing ( Math.Biosci.180, 141-160 ).The typical SIS and
SIR endemic disease models are modified to include a quarantine class Q, where
quarantine refers to individuals removed from the infectious class and who are
not mixing with the general population .In general , disease models use either a
simple mass action incidence term. This allows one to consider a scenario where
a student is kept home from school while infectious or where a sick worker stays
home from school but is not replaced.We will look closely at the stability of
equilibria along with some details in the proofs which illustrate several
commonly used methods and concepts, such as Liapunov functions,
uniform
persistence ,theory of limiting systems ,and Hopf bifurcation.
7. Friday, March 26, 2004. Time: TBA. Room: MP 3314.
Speaker: Professor Arkadi Nemiroviski, Visiting lecture, Technion Israel Institute of Technology, Haifa, Israel , presently visiting School of Mathematics, Georgia Institute of Technology. Click here for flyer.
Title: Mathematics of Robust Convex Optimization
Abstract: The data of real world Optimization problems usually are uncertain and not known exactly. Traditionally, small data uncertainties are merely ignored, in hope that the optimal solution corresponding to the nominal data will remain nearly feasible and nearly Optimal for the ¡§ true data as well. This hope in many cases is completely unrealistic. For example NETLIB LP problems, perturbations of clearly uncertain data as small as 0.01% make some of the constants, evaluated at the optimal solution ,more than 50% -in feasible.
Robust Optimization is a novel Optimization paradigm which form the beginning takes into account data uncertainly and looks for solutions which remain feasible for all realizations of the data from a given uncertainty set. The goal of the talk is to over view Uncertain Linear programming, Uncertain Conic Quadratic Programming, and uncertain semi definite programming. In the talk the speaker will present and discuss the aforementioned results along with the underlying facts (important by their own right) on tight tractable approximations of well structured semi infinite conic quadratic and semi definite inequalities. These facts are closely related to (and can be considered as extension of) recent results on the quality of semi definite relaxations of difficult combinatorial problems.
8.Thursday, April 1, 2004, Time: 2p.m-3p.m. Room no.2047 ( Russell Union )Visiting lecture, Professor Doron Lubinsky, School of Mathematics, Georgia Institute of Technology.
Title. Continuing the fraction.
Abstract. Much of the power of modern
mathematics lies in its ability to take limits : to add, multiply ,or devide
infinitely often.The speaker will focus on continued fractions ,which involve
infinitely many divisions. Number theory makes heavy use of continued fraction
expansions of power series. The speaker will compare and contrast the properties
of continued fractions in these two settings, and discuss the recent resolution
of the 1961 Baker-Gammel-Wills Conjecture.
9.Thursday, April 1, 2004. Time: 4P.M-5P.M Room Mp 3314:
Speaker: Professor Doron Lubinsky
Title:Bernsteins Constant in Approximation Theory
Abstract:Weierstrass proved in the 1880s that every continuous
function could be uniformly approximated by polynomials. How large must the
degree of the polynomial be to achieve a given accuracy? This has practical
implications in Numerical analysis, but also has a beautiful theory associated
with it. The speaker will review results of Jackson and Bernstein dating from
the period 1910 on words. In a paper published in Acta Mathematica in
1913,Bernstein proved that the rate of approximation of f(x) = mod (x) on [
-1,1] decays like C/n, where n is the degree of approximating polynomial.
Bernstein speculated what the value of C should be, but this was disproved using
numerical computation by Varga and Carpenter in 1985.A new representation for C
will be given and this will give a fully explicit form for the constant . Who
would believe that approximating the absolute value function by polynomials
would have so much to it?
10. Friday, April 9, 2004. Time: TBA. Room: MP 3314.
Speaker. Dr. K. N. Murty
Title: Some basic analogies between continuous and discrete First order systems and applications to Fundamental control.
Abstract: The relation between k-th order difference equation to the First order matrix difference system will be established and then the enology between Continuous and discrete systems will be presented. Fundamental results on Controllability, Realizability and observability on typical discrete system will be presented.
11. Thursday, April 15, 2004. Time: 2p.m-3p.m ( Russell Union ) Room no.2047
Speaker: Professor Sam B.Nadler Jr., Department of Mathematics, West Virginia University.
Title: A beautiful mind.
Abstract:
12. Friday April 16 2004, Time: 3p.m-4p.m. Room: MP 3314. Visiting lecture, Professor Sam B. Nadler Jr., Department of Mathematics, West Virginia University.
Title.Periodic points of locally expansive
mappings