Tuesdays, 4:30 - 5:30pm in JTB 130
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
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 two-dimensional ODEs and one-dimensional 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 multi-investgator grant. Topics that will be covered include:
to provide other perspectives.
$n \times n$ 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
n-dimensional 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
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.
of modeling cardiac arrhythmias distasteful, I will not spend any time on the modeling aspect of the system I will present.
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.
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: 3:00-4:00 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
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
Unfortunately, the usual proof of this theorem does not indicate
Riemann surface, which is, topologically, an oriented
compact manifold of dimension two (a many-holed torus).
When the ground field is finite, an algebraic curve resembles
the ring of integers in a number field-a number-theoretic object.
And when the ground field is the rational numbers, then
the elliptic curves (one-holed 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.
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.
cardiovascular problems. The main components of this process are
platelet aggregation and coagulation. Platelet aggregation involves
processes of cell-cell and cell-substrate adhesion and cell signaling
and response, all within the moving blood. Coagulation involves a
tightly-regulated 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.
Department of Mathematics
University of Utah
155 South 1400 East, JWB 233
Salt Lake City, Utah 84112-0090
Tel: 801 581 6851, Fax: 801 581 4148