David
Sanchez, Texas A&M University The speaker, a long-standing member of the ordinary differential equations (ODE) fraternity, has been studying why certain elementary topics which can serve as a platform for a study of more advanced ones, are neglected in the traditional introductory ODE course. These topics include existence of periodic solutions, resonance, onset of instability in two-dimensional models and others. In the talk, he will expand upon some simple examples; the audience level of understanding need only be minimal as reflected in a first-semester introductory ODE course. Bring questions!
Reinhard
Laubenbacher, New Mexico State University We live in the age of networks, from the WWW to networks of genes regulating cell function. A variety of mathematical tools have been applied to the study of networks, their topology and their dynamics. This talk will describe some new combinatorial tools for the study of networks and describe their application to communications, social, and biological networks.
Ricardo
Cortez, Tulane University There are many biological phenomena that involve elastic membranes moving in a fluid. Some examples are cells in the bloodstream, swimming organisms and blocked arteries. A computer simulation of these motions is very valuable for understanding these phenomena. The elements of a computational model are: (1) the biological nature of the forces generated on the membrane, and (2) the accurate description of the motion of the membrane and the fluid around it. The first element is typically developed by biologists and requires knowledge of muscle movement and physiology. The second element requires the solution of a complicated system of nonlinear differential equations. Here is where mathematics comes in. I will present computational models for the solution of this type of fluid/membrane interaction and will show the motion of swimming organisms and other examples. I will assume that the audience members have no knowledge of fluid dynamics or biology but are mathematics enthusiasts.
Victor
H. Moll, Tulane University We present a small number of open
problems that have originated in our work to evaluate some definite
integrals. In particular we discuss the current status of the research
projects of SIMU 2000:
José
Escobar, Cornell University In this talk, I will review how to obtain a maximum or a minimum of a real-valued function defined on a bounded domain in the Euclidean space. Then I will introduce the problem of finding a maximum or a minimum of a functional and discuss the difficulties of this problem. This kind of problem gives rise to a branch of mathematics known as the calculus of variations. Most problems that appear in physics and geometry can be embedded in the calculus of variations framework. A well know example is the isoperimetric problem, which will be presented in this talk.
Brian
Rodas, University of Maryland, College Park The Gröbner Walk is an algorithm designed to speed the computation of Gröbner basis of ideals with respect to elimination orders. However, depending on the complication and number of the initial forms, this may or may not prove to be faster than direct computation. The Evasive Walk is a perturbation of the Gröbner Walk that helps avoid big and complex initial forms, hopefully improving the speed of the computation. The talk will discuss a bare-bones implementation of the Evasive walk in comparison with the Gröbner Walk and direct computation using Buchberger's algorithm.
Rosa
C. Orellana, Dartmouth College The Hecke algebras of type A arise naturally in the study of knot theory, quantum groups, and Von Neumann algebras. Their relation to the symmetric and braid groups allows for their study using combinatorics and low dimensional topology. In this talk I will give an introduction to Hecke algebras of type A and B and show their relation to the symmetric group and the braid group (this groups will be defined in this talk). I will also construct a beautiful homomorphism from a specialization of the Hecke algebra of type B onto a reduced Hecke algebra of type A. This homomorphism has proven to be an useful tool to reduce questions about the Hecke algebra of type B To the Hecke algebra of type A. If time permits, I will give applications of this homomorphism.
David
Manderscheid, University of Iowa P-adic numbers can be used to study problems in number theory such as the question of when a polynomial equation in more than one variable with rational coefficients has solutions which are rational. Here p is a prime number and for each p there is the set of p-adic numbers. Given a p the set of p-adic numbers contains the set of rational numbers as a dense subset much as the rational numbers are dense in the real line. For p-adic numbers, though, distance is defined in terms of divisibility by p as opposed to the usual absolute value used to define distance on the real line. In this talk we will motivate the definition of p-adic numbers, explain their definition and give some applications to solving equations.
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