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

gave a talk on

Sturm-Liouville problems with eigenparameter dependent boundary conditions

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

gave a talk on

Legendre Elliptic Curves over Finite Fields

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

gave a talk on

Some Mathematical Aspects of Optical Bistability

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

The Third Annual Colloquiumfest

Friday, April 5, 2002, 3:30 p.m.

Professor Keith Promislow
Indiana University

gave a talk on

Pattern formation in Optical Parametric Processes

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

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

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

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

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

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

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.

Colloquium Talks 2002-2005

Colloquium Talks 2002/2003

Colloquium Talks 2000/2001

Colloquium Talks 1999/2000

Colloquium Talks 1998/99

Colloquium Talks 1997/98

Algebra and Logic Seminar

Cryptography & Coding Theory Student Seminar

Centre for Algebra, Logic and Computation

Last update: January 26, 2008 --------- created and maintained by Franz-Viktor Kuhlmann