# Seminars and Colloquia - Winter 2010

Dr. Zhuang Niu

Memorial University

Algebra Seminar

1:00 PM, Wednesday, April 21, 2010

HH-3017

"The classification of AH-algebras, II"

An AH-algebra is an inductive limit of homogeneous C*-algebras. This class of C*-algebras contains many naturally arising C*-algebras, for instance, UHF-algebras, irrational rotation algebras, and C*-algebra associated to certain minimal dynamical systems. The class of simple AH-algebras with a certain restriction on dimension growth were classified using the ordered K-group together with the pairing with the tracial simplex. In this talk, I will give a review on this classification theorem.

Dr. Zhuang Niu

Memorial University

Algebra Seminar

1:00p.m., Wednesday April 14, 2010

"The classification of AH-algebras"

An AH-algebra is an inductive limit of homogeneous C*-algebras. This class of C*-algebras contains many naturally arising C*-algebras, for instance, UHF-algebras, irrational rotation algebras, and C*-algebra associated to certain minimal dynamical systems. The class of simple AH-algebras with a certain restriction on dimension growth were classified using the ordered K-group together with the pairing with the tracial simplex. In this talk, I will give a review on this classification theorem.

Dr. Robert Gallant

Department of Mathematics Sir Wilfrid Grenfell College

Combinatorics Seminar

1:00 PM, Friday,April 9, 2010

HH-3026*"Finding discrete logarithms using additional information"*

The apparent computational difficulty of finding discrete logarithms in some groups is the basis for many cryptographic protocols. We motivate the discrete logarithm problem, and discuss algorithms for finding discrete logarithms. We discuss a connection of this research to error correcting codes.**Dr. Lisa Lix**

PhD, P. Stat. Associate Professor and Centennial Research Chair School of Public Health University of Saskatchewan

Statistics Seminar

10:00 a.m., Friday April 9, 2010

HH-3017*"Testing Multiple Outcomes in the Presence of Non-Normality and Variance Heterogeneity"*

In experimental investigations, a common problem involves testing for differences between two groups (i.e., treatment and control) on L > 2 correlated outcomes. This presentation focuses on resampling-based multiple-testing procedures and their performance to control the family wise error rate in the presence of non-normality and variance heterogeneity.**Dr. Mitja Mastnak**

Saint Mary's University

Colloquium

4:00 PM, Friday, March 26, 2010

SN-2105*"Hopf algebras in combinatorics"*

Hopf algebras are ubiquitous algebraic structures arising in many places in mathematics as well as in physics. In combinatorics they are often used to encode assembly and disassembly of discrete structures. I will outline the general theory of combinatorial Hopf algebras and illustrate it on several examples arising from various branches of mathematics,such as graph theory, representation theory, and free probability.

Dr. Yuan Yuan

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, March 26, 2010

HH-3017

"Stability and Hopf Bifurcation Analysis for Functional Differential Equation with Distributed Delay"

We consider a general functional differential equation with distributed delay. The local stability parameter regions are given and compared for a general distribution delay function and three frequently used distributed delays including Dirac, uniform and Gamma distributions.The global stability for a special system with finite delay is investigated by using Fluctuation method.Moreover, we discuss the Hopf bifurcation using normal form method, there the computation of the coefficients are given in the form of the corresponding characteristic equation explicitly. The examples and numerical simulation results are illustrated to verify the theoretical predictions.

Dr. Tom Baird

Memorial University

Algebra Seminar

1:00 PM, March 17 & 24, 2010

HH-3017

"An approach to equivariant cohomology using algebraic combinatorics, Part 2."

In their 1997 paper studying equivariant algebraic varieties,

Goresky-Kottwitz-MacPherson observed that in a range of interesting examples, including toric varieties and flag manifolds, the calculation of equivariant cohomology reduces to analyzing an associated combinatorial object now called a GKM-graph. This is a graph whose

vertices correspond to fixed points of the action, and whose edges are labeled by characters of the symmetry group. Their paper inspired a great deal of subsequent work, collectively known as "GKM theory", linking combinatorial algebra with equivariant topology. In two lectures aimed at non-experts, I will survey some of this theory.

This second lecture will be a survey of GKM theory including my recent work on GKM-sheaves over hypergraphs.

Mohammad Al-Jararha

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, March 19, 2010

HH-3017

"Population dynamics with age-dependent diffusion and death rates"

We talk about the population dynamics of a species with age structure in the case when the diffusion and death rate of the matured population are both age-dependent. A completely new model in terms of an integral equation is constructed. For unbounded spatial domain, we study the existence of traveling waves, while in bounded domain, we investigate the existence of positive steady-state solutions and their stability for different choices of birth function. As a by-product, we also prove rigorously the existence of real principle eigenvalue with positive eigenfunctions. Also, we present a numerical simulation.

Dr. Daniel Horsley

Memorial University

Combinatorics Seminar

1:00 PM, March 5 & 12, 2010

HH-3026

"Number Theory: Impartial Combinatorial Games"

Combinatorial games are a class of chanceless two player games in which players make alternate moves visible to their opponent. A combinatorial game is said to be impartial if both players can make the same types of moves in it. This talk will give a very gentle introduction to the theory of impartial combinatorial games.

Dr. Zhuang Niu

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, March 12, 2010

HH-3017

"Mean dimension and AH-algebras"

Mean dimension was introduced for topological dynamical systems by E. Lindenstrauss and B. Weiss. In this talk, this dynamics invariant will be adapted to an invariant (might depends on the inductive decomposition) for a certain class of inductive limits of homogeneous C*-algebras---the so called AH-algebras with diagonal maps. If any AH-algebra in this class has mean dimension zero (in particular if it has at most countably many extremal tracial states, or it is of real rank zero, i.e., projections generates the whole C*-algebra topologically), then the order on the projections is determined by traces. Note that there is no dimension restriction, either on the base space of each building block, or on its irreducible representations.

Dr. Qingwen Hu

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, March 5, 2010

"Optimal Vaccination Strategies During an Influenza Epidemic"

We present an optimal control model for optimal influenza vaccination strategies in a closed population. The model is based on an extended Kermack-McKendrick model with the vaccination policy a measurable function. The objective of the optimal control model is to describe the optimal vaccination strategies so that the total of the vaccination cost and the loss of infection is minimized. We obtain the dynamics of the controlled influenza epidemic and show that the optimal control is a nonsingular bang-bang control. We also give an algorithm for the solution of the optimal control problem using shooting method. Numerical simulations are carried out to illustrate the general results and to examine the effects of the parameters on the optimal vaccination strategies. The simulation shows that the ratio of the loss of infection and the vaccination cost has strong effect on the optimal strategies while the vaccination rate of newborns turns out to be insensitive. This is a joint work with Dr. Xingfu Zou.

Dr. Andrea Burgess

Memorial University

Combinatorics Seminar

1:00 PM, February 26, 2010

HH-3026

"Cycle decompositions of some families of graphs"

A graph G is said to be decomposable into cycles of length k if its edges may be partitioned into k-cycles. The study of cycle decomposition of the complete graph K_m dates back to the 19th century, when Kirkman proved that K_m decomposes into cycles of length 3 if and only if m is congruent to 1 or 3 modulo 6, and Walecki showed that K_m is decomposable into cycles of length m exactly when m is odd. The general problem of determining necessary and sufficient conditions for the existence of a k-cycle decomposition of K_m remained open until relatively recently; the final proof appeared in two parts, by Alspach and Gavlas in 2001 when k is odd, and by Sajna in 2002 when k is even. The study of cycle decompositions of complete graphs has been extended to related families of graphs, including complete multigraphs and complete equipartite graphs. Both of these families may be viewed as generalizations of the complete graph. In this talk, we review some known results on cycle decompositions of complete graphs, complete multigraphs and complete equipartite graphs, and present some original results.

Dr. Viqar Husain

University of New Brunswick

Departmental Colloquium

2:00 PM, February 19, 2010

HH-3017

"Quantum mechanics for quantum gravity"

A quantum theory of gravity is expected to provide a description of gravitation at the Planck scale, where the classical notions of metrics and manifolds is expected to break down. On the other hand, these structures lie at the basis of standard quantum theory. This tension is at the heart of the difficulty in formulating a theory of quantum gravity. I will describe a formulation of quantum mechanics that may hold the seeds of a solution, and describe some of its applications.

Dr. Abba Gumel

University of Manitoba

Departmental Colloquium

1:00 PM, February 19, 2010

HH-3017

"Mathematics of Infectious Diseases: The Case for The 2009 H1N1 Pandemic"

Mathematics has, historically, been used to gain insight into the transmission dynamics and control of infectious diseases, dating back to the work of Daniel Bernoulli in 1760s on smallpox. The talk will address the problem of the 2009 swine influenza (H1N1) pandemic, with particular emphasis on the burden of the disease in the province of Manitoba. A deterministic mathematical model (and its associated qualitative analyses) will be used to quantify the expected burden of the disease as well as to evaluate the potential impact of anti-H1N1 control strategies in effectively combatting the spread of the disease in the province.

Dr. S. H. Lui

University of Manitoba

Department Colloquium

4:00 PM, February 18, 2010

HH-3026

"Pseudospectrum and its applications"

The pseudospectrum of an operator is a generalization of its spectrum. Mainly due to the work of Nick Trefethen, it has become an important quantity for analyzing stability of non-normal systems with applications in numerical analysis, fluid mechanics, control theory, etc. We begin with an introduction to the topic followed by two mapping theorems for pseudospectra which generalize the spectral mapping theorem for eigenvalues. We also give asymptotic expansions of two quantities which characterize the sizes of pseudospectra. As an application of this theory, we solve the eigenvalue perturbation problem for an analytic function of a matrix. Some numerical examples illustrate the theory.

Dr. Mikhail Kochetov

Memorial University

Algebra Seminar

1:00 PM, Jan. 27 & Feb. 17, 2010

HH-3017

"Group gradings on simple Lie algebras of Cartan type"

We are interested in describing all group gradings on simple Lie algebras over an algebraically closed field $F$, i.e., all vector space decompositions of the form $L =bigoplus*{gin G}L*g$ where $L$ is a simple Lie algebra, $G$ is an abelian group, and $[L*g, L*h]subset L_{gh}$ for all $g,hin G$. A convenient tool for studying gradings in characteristic zero is their equivalence to diagonalizable subgroups of the automorphism group. It follows that, if two algebras have the same automorphism group, then the gradings on these algebras are in one-to-one correspondence. For example, one can use the classification of gradings on matrix algebras to obtain all gradings on Lie algebras of the series A, B, C, D. In order to make this work in positive characteristic, one has to consider automorphism group schemes. We will discuss restricted Lie algebras of Cartan type (except the contact case), which can be realized as differential operators on algebras of truncated polynomials. We will first classify all gradings on the truncated polynomial algebras and then use group schemes to pass to the Lie algebras of Cartan type.

Dr. Robert Bailey

Mathematics and Statistics, University of Regina

Combinatorics Seminar

February 12, 2010

1:00 PM - 2:00 PM

HH-3026

"Hamiltonian decompositions of hypergraphs"

A k-uniform hypergraph is like a graph, but where the``edges'' are k-sets, rather than pairs, of vertices. There are various ways in which one can define a Hamilton cycle in a hypergraph. Just as with graphs, for each notion of Hamilton cycle, one can ask for a Hamiltonian decomposition of a hypergraph, i.e. a partition of the edge set into Hamilton cycles. We will focus on one particular notion of Hamilton cycle, and on the complete k-uniform hypergraph, discussing a conjecture which is very natural and easy to state but incredibly hard to solve, but which has been verified in some (very) special cases.This talk includes joint work with B. Stevens, as well as results due to M. Meszka and A. Rosa, and due to J. R. Johnson.

Dr. Xiuxiang Liu

South China Normal University

Departmental Colloquium

2:00 PM, January 29, 2010

HH-3017

"Global Dynamics of A Predator-Prey Model"

We first give a brief review of predator-prey models in

population biology. Then we introduce a predator-prey model

with Hassell-Varley-Holling functional response, which is supported by the first experimental evidence discriminating between ratio-and prey-dependence in a natural setting with unconfined predators and prey. Our qualitative anlaysis for this model shows that the predator coexists with prey if and only if the predator's growth ability is greater than its death rate, that the extinction of both predator and prey populations is impossible, and that the local stability of the positive steady state implies the global one when the predator interference is large. Further, the instability of the positive equilibrium implies the global stability of the limit cycle when the predator interference is equal to 0.5. Some numerical simulations will also be presented to illustrate our analytical results.

Dr. Xiaoqiang Zhao

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, January 22, 2010

HH-3017

"Global Attractivity in A Class of Nonmonotone Reaction-Diffusion Equations with Time Delay"

The global attractivity of the positive steady state is established for a class of nonmonotone time-delayed reaction-diffusion equations subject to the Neumann boundary condition via a fluctuation method. This result is also applied to three population models.

Yijun Lou

Memorial University

Applied Dynamical Systems Seminar

1:00 PM, January 15, 2010

HH-3017

"A reaction-diffusion malaria model with incubation period in the vector population"

Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period (EIP) of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction-diffusion model. We then define the basic reproduction ratio and show that this ratio serves as a threshold parameter that predicts whether malaria will spread. Furthermore, a sufficient condition is obtained to guarantee that the disease will stabilize at a positive steady state eventually in the case where all the parameters are spatially independent. Numerically, we show that the use of the spatially averaged system may highly underestimate the malaria risk. The spatially heterogeneous framework in this work can be used to design the spatial allocation of controllable resources. This is a joint work with Dr. Xiaoqiang Zhao.

Shannon Starr

Rochester University

Departmental Colloquium

2:00 PM, January 11, 2010

"The Length of the Longest Increasing Subsequence in a Random Mallows Permutation"

Ulam proposed studying the length of the longest increasing subsequence in a random permutation. For instance, for the permutation 5 2 8 4 1 9 7 6 3, written in one line notation, 5 8 9 is a longest increasing subsequence so the length is 3. Henceforth we write l.i.s. for “longest increasing subsequence. “Writing ℓ(n) for the length of the l.i.s. of a random permutation in S_n, Hammersley proved that ℓ(n)/ sqrt(n) converges to a non-random limit, c, almost surely. In two independent papers Vershik and Kerov, and Logan and Shepp proved that c equals 2. Recently, Borodin, Diaconis and Fulman asked for the length of the l.i.s. for another class of random permutations, called Mallows random permutations. These arise in statistics and in algebra. With Carl Mueller, we calculated the law of large numbers for this. An interesting question, which is still open, is to find the analogue of the central limit theorem. For uniform random permutations, that was done by Baik, Deift and Johannson, and it was a major discovery connecting random permutations to random matrices.