COLLOQUIUM
of the
Mathematical Sciences Group
at the Department of Computer
Science
University of Saskatchewan
Colloquium chair:
Salma Kuhlmann
Colloquium Talks 2001/2002
Friday, November 30, 2001, 3:30 p.m.
Professor Gordon
Sarty
Department of Psychology,
Saskatoon
gave a talk on
BOLDfold for fMRI: Statistics or Pattern Recognition?
This event was organized jointly with the Cognitive and Neurosciences
Seminar Department of Psychology.
Friday, January 4, 2002, 3:30 p.m.
Professor Eric Neufeld
Department of Computer Science,
Saskatoon
gave a talk on
A variation on the Puzzle of the Two Envelopes
Friday, January 11, 2002, 4:00 p.m.
Professor Patrick Browne
Saskatoon
gave a talk on
Sturm-Liouville problems with eigenparameter dependent boundary
conditions
Abstract:
This talk gave an overview of results concerning existence and
asymptotes of eigenvalues, and oscillation theory for Sturm-Liouville
problems of the type
-(py')' + qy = lry
with boundary conditions
at x=0: (py'/y)(0) = cota
at x=1: (py'/y)(1) = g(l)
for various functions g(l).
Friday, January 25, 2002, 3:30 p.m.
Professor Bruce Watson
University of Witwatersrand, South Africa (presently visiting U of S
and U of C)
gave a talk on
Inverse Spectral Problems
The classical problems of inverse spectral theory are: given two spectra
from a Sturm-Liouville problem given by changing the left hand boundary
condition uniquely determine the potential and the right hand boundary
condition; given the Weyl m-function for a Sturm-Liouville problem
uniquely determine the potential and both boundary conditions; given a
spectrum and corresponding `norming constants' determine the potential
and boundary conditions.
These results are well known from the 1950's for the standard
Sturm-Liouville problem. We show the extension of these results to
Sturm-Liouville problems with boundary conditions depending on the
eigenparameter.
Friday, March 1, 2002, 3:30 p.m.
Dr. Roland Auer
Saskatoon
gave a talk on
Legendre Elliptic Curves over Finite Fields
Abstract:
The Legendre elliptic curve with parameter l
is given by the equation
y2 = x (x - 1) (x - l) .
When considered over a finite field (of odd characteristic), it
specifies a finite abelian group containing a 2x2-subgroup. Joint work
with Jaap Top revealed that, vice versa, (almost) every possible group
order (of an elliptic curve) which is divisible by 4 can be realised by
a Legendre model. Since the Legendre family is given by only one
parameter, this simplifies the search for elliptic curves with an order
suitable for ElGamal's public key cryptosystem.
Another application is to coding theory:
The mentioned result implies the existence of a genus 3 curve with many
points over every finite field having a 3-power number of elements.
Using Goppa's construction then yields an error-correcting code with
good parameters.
Friday, March 15, 2002, 3 p.m.
Professor Holger Teismann
Saskatoon
gave a talk on
Some Mathematical Aspects of Optical Bistability
Abstract:
Optical systems which exhibit bistability - i.e., which respond to a
given input by two stable output states - can serve as optical switches
and data storage devices and therefore as potential building blocks of
all-optical computers. The purpose of this talk is to describe the
occurence of optical bistability in a feedback configuration (ring
cavity) with a nonlinear optical medium. The mathematical model consists
of an infinite-dimensional dynamical system, defined by a sequence of
solutions to a nonlinear Schroedinger equation.
Friday, March 22, and Saturday, March 23, 2002
Friday, April 5, 2002, 3:30 p.m.
Professor
Keith
Promislow
Indiana University
gave a talk on
Pattern formation in Optical Parametric Processes
Abstract:
The transparency and the weak nonlinear and dispersive properties
of fiber optic glass make it ideal for pulse propagation over great
distance, but very poor for manipulation of coherent radiation. It
is the strong nonlinear and dispersive properties of Chi-2 optical
crystals which make them well suited for building the switches and
routers of optical networks. The tunability, or optical parametric
resonance, afforded by these devices corresponds to a rich class
of mathematical models for three-wave interaction. I will give
an overview of a rigorus mathematical treatment of pulse-pulse
interactions and surprisingly robust transverse pattern formation
in these important devices.
Friday, April 19, 2002, 3:30 p.m.
Professor Murray Marshall
The Mathematical Sciences Group, Department of Computer Science
gave a talk on
Optimization of polynomial functions using semi-definite
programming
Abstract:
Recently progress has been made (by N.Z. Shor, P.A. Parrilo,
P. Parrilo & B. Sturmfels and by J.B. Lasserre) in the development of
fast algorithms for optimizing polynomials. The main idea is to relax
the problem to a simpler problem (involving sums of squares and moment
sequences) which can be solved by semidefinite programming. The method
has potential application in control theory, for example. In most cases
the method produces exact results and dramatically outperforms existing
algebraic methods. The talk, which is a survey of this work, involves a
nice mixture of real algebraic geometry, functional analysis and
optimization.
Friday, April 26, 2002, 3:30 p.m.
Professor
Doug
Farenick
University of Regina
gave a talk on
Young's Inequality
Abstract:
A variant of the arithmetic-geometric mean inequality is Young's
inequality: if p,q are positive real numbers such that 1/p + 1/q = 1,
then |ab| is less or equal to
1/p |a|p
+ 1/q |b|q, for all complex
numbers a and b.
In this lecture, I will survey recent formulations of Young's inequality
at the level of compact operators and operator norms.
Friday, May 3, 2002, 3:30 p.m.
Professor Chris Soteros
The Mathematical Sciences Group, Department of Computer Science
gave a talk on
Eigenvalue problems in algebraic graph theory
Friday, May 10, 2002, 2 p.m.
Professor Winfried
K. Grassmann
Department of Computer Science,
Saskatoon
gave a talk on joint work with
Dr. Steve Drekic,
Department of Statistical and Actuarial Science,
University of Waterloo:
An Analytical Solution for a Tandem Queue with Blocking
Abstract:
The model considered in this paper involves a tandem queue with
two waiting lines, and as soon as the second waiting line reaches a
certain upper limit, the first line is blocked. Both lines have
exponential servers, and arrivals are Poisson. The objective is to
determine the joint distribution of both lines in equilibrium. This
joint distribution is found by using generalized eigenvalues.
Specifically, a simple formula involving the cotangent is derived. The
periodicity of the cotangent is then used to determine the location of
the majority of the eigenvalues. Once all eigenvalues are found, the
eigenvectors can be obtained recursively. The method proposed has a
lower computational complexity than all other known methods.
Thursday, May 23, 2002, 3:30 p.m.
Professor Allen Herman
University of Regina
gave a talk on
Schur indices of crossed product algebras
Abstract:
A crossed product algebra over a field K is a special type
of central simple algebra over K that comes with a nice presentation
in terms of a Galois extension and a cocycle of its Galois group.
Being a central simple algebra over K, it follows from the
Artin-Wedderburn theorem that each crossed product algebra is isomorphic
to Mn(D), for some finite-dimensional division algebra D with
center K. The basic question that arises is that of Schur index
calculation: can the dimension of the division algebra D be determined
from the nice presentation of the crossed product algebra? The most
beautiful case of a positive answer occurs when the Galois extension is
cyclic and the field is a global field. This is a consequence of the
Hasse Norm Theorem and the Grunwald-Wang theorem from class field
theory.
In this talk we will illustrate this classical theory by working
through some Schur index calculations. We will conclude with
indications of the connections between these classical ideas and some
modern work concerning Brauer groups, Galois cohomology, and G-algebras.
Friday, May 24, 2002, 3:30 p.m.
Professor Javad Tavakoli
Saskatchewan Indian Federated College (SIFC)
gave a talk on
Topology and smallness in a category of sheaves
Abstract:
In this talk we will show that the class of maps generated by dense
subobjects for a given Grothendieck topology on a partially ordered set
P consists of maps which are "small" in the Joyal-Moerdijk
sense. We use this to construct a dense sup-lattice within P. Then we
show that the collection of these sup-lattices is a completion of P.
Friday, May 31, 2002, 3:30 p.m.
Professor Patrick Browne
The Mathematical Sciences Group, Department of Computer Science
gave a talk on
Staeckel Determinants
Abstract:
Staeckel determinants are determinants of real valued functions which
arise in linked systems of ordinary differential equations. They have a
special form in that the functions in the ith row of the determinant are
functions of the variable xi, so that ultimately the
determinant is a function of the n-dimensional variable x =
(x1, ... , xn). A standard assumption is to demand
that the determinant be positive as a function of this variable x. Under
this assumption the determinants have interesting and surprising
properties which will be revealed in the lecture.
Last update: January 26, 2008
--------- created and maintained by Franz-Viktor Kuhlmann