Fall 2001 Tuesdays, 4:30  5:30pm in JTB 130 Math 69603 The goal of this colloquium is to encourage interaction among graduate students, specifically between graduate students who are actively researching a problem and those who have not yet started their research. Speakers will discuss their research or a related inrtoductory topic on a level which should be accessible to nonspecialists. The discussions will be geared toward graduate students in the beginning of their program, but all are invited to attend. This invitation explicitly includes undergraduate students. Talks will be held on Tuesdays at 4:30pm in JTB 130, unless otherwise
noted.
Title: Periodic Stimulus and the Single Cell
(APD) immediately following each stimulus. Experiments demonstrate that the rhythms generated by such stimulus protocols can vary widely, depending on frequency and amplitude of the stimulus. A theoretical approach based on the APD is capable of explaining some of the experimental observations but a complete understanding of the parameter dependence is beyond the scope of the APD approach. We discuss some fundamental problems with the APD approach and propose a new one dimensional map that relies on the presence of a one dimensional slow manifold in the dynamics. This slow manifold map extends the understanding offered by the APD approach to include an explanation of Wenckebach rhythms. In addition, the bifurcation structure of the map provides a unified description of the parameter dependence that agrees fairly well with experimental observation. Some familiarity with twodimensional ODEs and onedimensional maps will be helpful.
Speaker: Aaron Bertram, Graeme Milton, Cindy Phillips, and Anurag Singh Title: Preparing a Successful Grant Proposal Abstract: This talk is for graduate students who may be interested in getting
may be applying for a grant for the first time, and for other interested faculty. The focus will be on applying for a regular NSF individual investigator mathematics research grant, rather than on a large multiinvestgator grant. Topics that will be covered include: to provide other perspectives. Sept. 11
$n \times n$ invertible real matrices. For finite dimensional representations of GL(n, R), it's completely elementary and dates back to Schur. For infinite dimensional representations, the interaction is of a completely different (and more sophisticated) flavor. It involves the geometry of the desingularization of the variety of ndimensional nilpotent matrices. Speaker: Fumitoshi Sato Title: Symmetric Functions Abstract: This talk is about symmetric functions which are the generalization of
Speaker: Bob Guy Title: The Stokes Paradox Abstract: Many classical problems in fluid dynamics motivated the
One such classic problem is to find the force acting on a solid body moving in a fluid, given the velocity of the body. From a reduction of the equations governing viscous fluid flow, in
I will go over the conceptual ideas of the problem and the reasoning
Oct. 2
intersection multiplicity of two algebraic sets which meet at a point. The definition should give a measure of the order of tangency at the point and generalize the classical definitions for intersections of curves in the plane. Attempts to define intersection multiplicities in a general algebraic setting have led to several interesting conjectures and questions in Commutative Algebra. In this talk I will discuss intersections of curves in the plane and what properties the multiplicity should satisfy, show how they can be generalized higher dimension, and describe some questions which have developed from these ideas. Oct. 9
Oct. 16
Oct. 23
of modeling cardiac arrhythmias distasteful, I will not spend any time on the modeling aspect of the system I will present. Oct. 30
for work in mathematics as such. Using this observation as a starting point I shall discuss several questions related to the practice of mathematics that might be of interest to anyone interested in understanding what it is to do research in mathematics. In the course of the discussion I shall give examples of what I consider to be great achievements in the fields I work in. Nov. 6
Nov. 13
structure. After going over the basic notions of hyperbolic geometry we'll learn how to construct hyperbolic structures on surfaces and see what the space of all such structures looks like. With that completed we'll try to answer the question above. Nov. 16 (SPECIAL COLLOQUIUM) Place and Time: 3:004:00 JTB 110 Speaker: Carl Cowen, Professor of Mathematics, Purdue University Title: Rearranging the Alternating Harmonic Series Note: Professor Cowen is particularly interested in meeting with students
Abstract:
school children that it comes as a shock to those studying college level mathematics that NOT all 'natural extensions' of the law are true! One of the first instances that we see the failure of an extended commutative law of addition is in infinite series. Often in the introduction to infinite series in calculus, one sees Riemann's Theorem:
Unfortunately, the usual proof of this theorem does not indicate
what the
Nov. 20
Riemann surface, which is, topologically, an oriented compact manifold of dimension two (a manyholed torus). When the ground field is finite, an algebraic curve resembles the ring of integers in a number fielda numbertheoretic object. And when the ground field is the rational numbers, then the elliptic curves (oneholed tori) become fascinating for their unpredictable numbers of rational points. I'd like to touch on all of these, explain a little bit of history, and explain some of their practical uses. Nov. 27
that graphs of this type are intrinsically linked or intrinsically knotted. We will prove the first result above, and briefly outline the proof of the second. We will also try to generalize these results by asking the questions, "Which graphs are intrinsically linked (knotted)?" I also want to advertise the other knot theory talk I will be giving that day. I will be presenting an introduction to knot theory at the undergraduate colloquium in AEB 350 at 12:55. This first talk requires no technical mathematics. Dec. 4
cardiovascular problems. The main components of this process are platelet aggregation and coagulation. Platelet aggregation involves processes of cellcell and cellsubstrate adhesion and cell signaling and response, all within the moving blood. Coagulation involves a tightlyregulated network of enzyme reactions with the important feature that many of the key reactions occur on surfaces (e.g. platelet surfaces), not in the bulk fluid, while transport of the reactants occurs in the fluid. Coagulation results in the formation of a polymer mesh around the aggregating platelets. I will introduce listeners to the biology of blood clotting, will outline several aspects of our efforts to model these complex dynamic biological systems, and will discuss some of the modeling and computational challenges in this work. Gory pictures and movies will be shown.
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