# Fall 2008

Dr. Shengda Hu

Candidate for Tenure-Track Position in Algebraic Topology

University of Waterloo

Friday, December 19, 2008

2:00 p.m., HH-3026

"Localization in twisted equivariant cohomology"

We will introduce equivariant cohomology and the twisted version of it, for manifolds with an action of Lie group. For ordinary equivariant cohomology, one has the important theorem of Atiyah-Bott localization. We will discuss the

corresponding twisted version. Time permitting, we will compute an example with the twisted localization theorem.

Dr. Robert Smith

Department of Mathematics

University of Ottawa

2:00 p.m., HH-3026

"Determining Effective Spraying Periods to Control Malaria via Indoor Residual Spraying in Sub-Saharan Africa"

Indoor residual spraying - spraying insecticide inside houses to kill

mosquitoes - is an important method for controlling malaria vectors in sub-Saharan Africa. We propose a mathematical model for both regular and non-fixed spraying, using impulsive differential equations. First, we determine the stability properties of the nonimpulsive system. Next, we derive minimal effective spraying intervals and the degree of spraying effectiveness required to control mosquitoes when spraying occurs at regular intervals. If spraying is not fixed, then we determine the “next best” spraying times. We also consider the effects of climate change on the prevalence of mosquitoes. We show that both regular and nonfixed spraying will result in a significant reduction in the overall number of mosquitoes, as well as the number of malaria cases in humans. We thus recommend that the use of indoor spraying be re-examined for widespread application in malaria-endemic areas.

Dr. Tom Baird

University of Oxford

Tuesday, December 9, 2008

2:00pm, HH-3017

"Moduli of flat connections over 2-manifolds"

The moduli of flat connections over Riemann surface is a rich subject with applications to mathematical physics, low dimensional topology, moduli of curves, representations of loop groups and geometric Langlands. I will review this theory and then describe what happens when the Riemann surface is replaced with a nonorientable surface.

Yanqing Yi

Division of Community Health & Humanities

Memorial University of Newfoundland

Seminar

Friday, December 12, 2008

1:30pm, HH-3017

"Asymptotically efficient estimation for response adaptive designs of clinical trials"

A response adaptive design of clinical trial sequentially modifies the

treatment allocation probability based on the treatment and response information so far accumulated in the trial, for the purpose of assigning more trial patients to the potentially superior treatment. However, such an adaptation of treatment allocation probabilities, as opposed to the traditional balanced randomization, leads to dependent samples, and consequently the traditional statistical methods cannot be directly applied to response adaptive designs.

The issue of asymptotic efficiency of estimation is examined for response adaptive designs of clinical trials. The asymptotic lower bound of exponential rates for consistent estimators is established. Under certain regularity conditions, it is shown that the maximum likelihood estimator achieves the asymptotic lower bound for response adaptive trials with dichotomous responses. Furthermore, it is proved that the maximum likelihood estimator of the treatment effect is asymptotically efficient in the Bahadur sense for response adaptive clinical trials.

Cameliza Navasca

Department of Mathematics and Statistics

Clarkson University

Potsdam, New York

Departmental Colloquium

Friday, November 28, 2008

2:00pm, HH-3017

“Tensors and their Applications”

In this talk, I will present some new techniques for tensor decomposition and some applications. First, I will define what tensors are and describe several tensor models, namely PARAFAC/CANDECOMP and Block Tensor Decomposition (BTD). These tensor models rely on numerical methods in optimization and numerical linear algebra. Current methods like the Alternating Least-Squares are inefficient and inadequate for some applications. I will discuss our novel numerical methods and demonstrate their important attributes. Since tensor decompositions have been playing a major role in advancing signal processing and communications, some of the numerical examples will be motivated by signal processing applications. I will also include some applications in scientific computing.

Mr. Yijun Lou

Department of Mathematics and Statistics

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, November 28, 2008

1:00pm, HH-3017

“Threshold Dynamics in A Time-Delayed Periodic SIS Epidemic Model ”

The global dynamics of a periodic SIS epidemic model with maturation delay is investigated. We first obtain sufficient conditions for the single population growth equation to admit a globally attractive positive periodic solution. Then we introduce the basic reproduction ratio for the epidemic model, and show that the disease dies out when this ratio is less than one, and the disease remains endemic when this ratio is greater than one. Numerical simulations are also provided to confirm our analytic results.

Dr. Chunhua Ou

Department of Mathematics and Statistics

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, November 21, 2008

1:00pm, HH-3017

“How Many Consumer Levels Can Survive in a Chemotactic Food Chain”

We investigate the effect and the impact of predator-prey interactions, diffusivity and chemotaxis on the ability of survival of multiple consumer levels in a predator-prey microbial food chain. We aim at answering the question of how many consumer levels can survive from a dynamical system point of view. To solve this standing issue on food-chain length, first we construct a chemotactic food chain model. A priori bounds of the steady state populations are obtained. Then under certain sufficient conditions combing the effect of conversion efficiency, diffusivity and chemotaxis parameters, we derive the co-survival of all consumer levels, thus obtaining the food chain length of our model. Numerical simulations not only confirm our theoretical results, but also demonstrate the impact of conversion efficiency, diffusivity and chemotaxis behavior on the survival and stability of various consumer levels.

Dr. David Pike

Department of Mathematics and Statistics

Memorial University of Newfoundland

Combinatorics Seminar

Thursday, November 13, 2008

3:30pm, AA-1049

“RAINBOW SMELT IN NEWFOUNDLAND - A GRAPH THEORETIC PERSPECTIVE ON GENETIC CONNECTIVITY ”

We compare various applications of graph theory to ecological research (such as landscape connectivity models, as well as population graph models). Further, we introduce two new models of connectivity measurement, one that entails an index of coincidence of genetic data collected from sample populations, and another that is based on pairwise comparisons of individuals.

We focus our analysis on a case study of rainbow smelt from Newfoundland coastal locations and evaluate the relative effectiveness of the graph theoretic techniques at discerning metapopulations and the degree of connectivity between population sampling sites.

We find that neither of the previous two models successfully distinguishes metapopulations within our dataset. However, each of the two models that we introduce do perform well at this task.

This is joint work with: Y. Zou, I.R. Bradbury, P.V.R. Snelgrove, P. Bentzen,

Melinda Buchanan

The University of Queensland

Combinatorics Seminar

Friday, November 7, 2008

4:00pm, HH-3026

“Designs, coverings and not-the-Bruck-Ryser-Chowla theorem ”

A (v,k,l)-pair covering consists of a set V of v points and a collection of k-subsets of V, called blocks, such that each pair of elements of V occurs in at least l of the blocks. I will discuss some new results on the non-existence of certain pair covering designs and explain why these results are intriguing (in the authors' opinions). First I'll give a gentle introduction to the area - so no expertise required! (Joint work with Darryn Bryant, Barbara Maenhaut, Daniel Horsley and Victor Scharaschkin.)

Dr. Yuri Bahturin

Department of Mathematics and Statistics

Memorial University of Newfoundland

Algebra Seminar

Wednesday, November 5, 2008

1:00pm - 1:50pm, HH-3017

“Jordan gradings on the full matrix algebras ”

Any associative algebra can be made into a Jordan algebra if we replace the original product xy by a "symmetrized" product xy+yx. In a recent paper with M. Bresar (Slovenia) and I. Shestakov (Brazil) we studied the group gradings of Jordan algebras attached to the associative algebras, for example to the classical matrix algebras. Since the gradings of associative algebras are explored much better, we try to reduce Jordan gradings to the associative ones. This is shown to be possible in a very wide range of cases, thanks to the new techniques coming from the theory of so called functional identities. I plan to briefly explain the results of this theory and to show how they work when applied to the gradings of Jordan algebras.

Dr. Xiao Wang

University of Defense Technology, China

Colloquium

Friday, November 7, 2008

2:00pm, HH-3017

“A new approach to the existence and uniqueness of almost periodic solution ”

Since it is very difficult to obtain the compactness of an almost periodic function set, many classical methods controlled by compact conditions such as Schauder's fixed point theorem and the coincidence degree are not able to be applied to solve almost periodic cases. Therefore, it becomes more complicated to investigate the existence, nonexistence and uniqueness of positive almost periodic solution for a certain model by the traditional methods. In this paper, the authors establish a new fixed point theorem without the compact conditions. As its application, some sufficient conditions of the existence, nonexistence and uniqueness of positive almost periodic solution for a model of Hematopoiesis are obtained. Also, the technique used here is different from usual methods employed to solve almost periodic cases such as the contraction mapping principle and Lyapunov functional.

Ms. Rebecca Keeping

Department of Mathematics and Statistics

Memorial University

Combinatorics Seminar

Tuessday, October 28, 2008

3:30pm, AA-1049

“A Review of the Watchman's Walk Problem”

A museum is attempting to guard each of its rooms. Rather than having guards placed at every room in a dominating set, Hartnell, Rall, and Whitehead (1998) considered the problem of having one watchman who must walk around the museum in such a way that the visited rooms form a dominating set. As the goal is to minimize the amount of time for which any room is unobserved, we are looking for a `minimum closed dominating walk' for a given graph. This talk will introduce the problem and outline some initial results, including upper bounds as well as constructions for certain graphs. The watchman's walk problem on circulant graphs will also be discussed.

Dr. Danny Dyer

Department of Mathematics and Statistics

Memorial University

Combinatorics Seminar

Thursday, October 23, 2008

3:00pm, AA-1046

“Two coloured path decompositions”

Consider a complete graph with two edges between each pair of vertices, one coloured red, and one coloured blue. Given a path of equal numbers of red and blue edges, can you decompose the graph into copies of that path? That is, can you partition the edge set of the graph into identical edge-disjoint copies of the path? We will investigate infinite families of paths of fixed lengths. This talk will discuss joint work with Brian Alspach, Angela Beck, and Kathy Heinrich.

Renzo A. Piccinini

Department of Mathematics and Statistics

Dalhousie University

COLLOQUIUM

Friday, October 24, 2008

2:00pm, HH-3017

“Conjugacy Classes of Gauge Groups”

Please click here to view the abstract.

Ms. Rebecca Keeping

Department of Mathematics and Statistics

Memorial University of Newfoundland

Combinatorics Seminar

Thursday, October 16, 2008

3:30pm, AA-1049

“Maximum k-Limited Packings in Trees.”

A fast food restaurant is known to service customers from its own business district as well as from neighbouring districts, and so the overarching service area can only support a limited number of restaurants before market saturation occurs. If franchisers want to have as many restaurants as possible without flooding the market, how should locations be selected?

This problem can be modelled with graph theory, using k-limited packings: that is, sets S ⊆ V (G) satisfying |N [v] ∩ S| ≤ k for all closed vertex neighbourhoods N [v] in a graph G. This talk will introduce the concept of k-limited packings in graphs and will outline an algorithm for finding maximum 3-limited packings in trees.

Dr. Wengu Chen

Beijing Institute of Applied Physics and Computational Mathematics

Colloquium

Friday, October 17, 2008

2:00pm, HH-3017

“Multilinear Estimates and Applications to KdV-type Equations”

By the fixed point argument, the well-posedness of initial value problem (IVP) for some dispersive equations is reduced to proving multilinear estimates in Bourgain's spaces. There are two approaches to accomplish the proof of multilinear estimates. One is used by Bourgain and then developed by Kenig, Ponce and Vega for the cubic KdV equation. The other is Tao's [k;Z]-multiplier norm method. This talk is devoted to giving some comparison between these two approaches in verifying multilinear estiamtes, and exploring some applications to IVP for KdV-type equations.

Dr. Edgar Goodaire

Department of Mathematics and Statistics

Memorial University of Newfoundland

Combinatorics Seminar

Thursday, October 9, 2008

3:30pm, AA-1049

“Group-based Latin Squares”

My recent work in loop rings has led me to Latin squares (of order n, say) whose entries are functions of an abelian group of order n. For example, if the Latin square is named α and the entries of both α and an abelian group (G,*) of the same order are the integers 1, 2, 3,...,n, perhaps α(α(i,i)*j,i) = α(i,i)*α(i,j). Finding "solutions" - that is, finding all α satisfying such a condition - is proving a daunting task. Perhaps some members of the audience can help.

Ms. Luju Liu

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, October, 3, 2008

1:00pm, HH-3017

“A Tuberculosis Model With Seasonality”

A tuberculosis (TB) model incorporating seasonality is developed and analyzed. It is shown that the disease-free periodic solution is globally asymptotically stable and the disease always dies out when the basic reproduction ratio is less than one, and there exists at least one positive periodic solution and the disease is uniformly persistent when this ratio is greater than one. Numerical simulations indicate that there is a unique positive periodic solution which is globally asymptotically stable in the latter case.

Dr. Daniel Horsley

Department of Mathematics and Statistics

Memorial University of Newfoundland

Combinatorics Seminar

Thursday, October, 2, 2008

3:30pm, AA-1049

“A solution to Alspach's problem for complete graphs of large odd order.”

In 1981 Brian Alspach posed the problem of proving that a complete graph of order n can be decomposed into edge-disjoint cycles of specifed lengths m1;m2,...,mt whenever there is no obvious reason that this cannot be done. So far no-one has managed to prove this in general.

Darryn Bryant and I have been working at this problem for some time and have proved two lemmas which allow us to get new cycle decompositions of complete graphs from existing cycle decompositions of complete graphs. We can use these lemmas to show that to answer Alspach's problem in general, it suffices to answer it only for lists of cycle lengths which satisfy certain very restrictive properties. This reduction has allowed us to settle Alspach's problem for all sufficiently large odd values of n.

In this talk I will give a description of these two lemmas and of our reduction of the problem, and will briefy mention our solution for large odd n.

Dr. Dariusz Dereniowski

Department of Algorithms and System Modeling

Gdansk University of Technology

Combinatorics Seminar

Thursday, September 25, 2008

3:30pm, AA-1049

“Using edge rankings for searching in partial orders.”

Given a simple graph G, an edge ranking of G is such a function, mapping the set of edges into integers, that each path connecting two edges of the same color contains an edge of a bigger color. The goal is to find an edge ranking of G using the minimum number of colors. We consider the connection between this optimization problem and the problem of searching elements in partial orders. In particular we are interested in Â nding the cases of the searching problem which can be solved using the graph ranking approach.

Dr. David Pike

Department of Mathematics and Statistics

Memorial University of Newfoundland

Combinatorics Seminar

Thursday, September 18, 2008

3:30pm, AA-1049

“Hamiltonicity and Restricted Block-Intersection Graphs of t-Designs”

Given a combinatorial design D with block set B, its traditional block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and only if b1 and b2 have non-empty inter-section. We consider the S-block-intersection graph, in which two vertices b1 and b2 are adjacent if and only if |b1 ∩ b2| ∈ S. As our main result we prove that {1,2,...,t-1}-block-intersection graphs of t-designs with parame- ters (v,t+1,λ ) are hamiltonian whenever t≥3 and v ≥ t + 3, except possibly when (v, t) ∈ {(8, 5), (7, 4), (7, 3), (6, 3)}.

This is joint work with Robert Vandell and Matthew Walsh of Indiana- Purdue University at Fort Wayne.

Mr. Jian Fang

Memorial University of Newfoundland

Applied Dynamical Systems Seminar

Friday, September 19, 2008

1:00pm, HH-3017

“Spreading Speeds and Traveling Waves for Nonmonotone Time-delayed Lattice Equations”

The spreading speed and its coincidence with the minimal wave speed are established for a nonlocal and nonmonotone time-delayed lattice model on mature population in a patchy environment. The uniqueness (up to translation) of traveling waves with non-minimal speed is also obtained.

Dr. D. de Werra

Ecole Polytechnique Fedrale de Lousanne (EPF)

Switzerland

Colloquium

Thursday, September 11, 2008

1:00-2:00pm, HH-3017

“Graph transformations and peseudoboolean reduction ”

Graph transformations have been developed either to decrease the stability number of a graph (i.e., the maximum size of an independent set of vertices) by a fixed amount or to reduce the number of vertices without changing the stability number. They were inspired by a pseudoboolean formulation of the maximum stable set problem and used the concept of conflict graph introduced by P.L.Hammer. These constructions were justified afterwards with purely graph theoretical arguments. A close examination of these transformations has exhibited a strong connection with operations designed to merge specific pairs of vertices in some classes of perfect graphs without changing the chromatic number. We shall examine the case of the magnet reduction applied whenever two adjacent vertices have their sets of proper neighbors completely linked. Connections with a merging procedure for a generalization of even pairs of vertices (all induced chains between them have an even length) will be exhibited Open questions related to the interpretation of the reduction of the stability number in some classes of perfect graphs will be presented. Lsne, sept 08