# Fall 2009

**Dr. Junping Shi**

College of William and Mary, Virginia, USA

Departmental Colloquium

2:00 PM, December 14, 2009

HH-3017*"Bifurcation and pattern formation in spatial predator-prey systems*"

Predator-prey interaction is a basic interspecies relation for ecological and social models. We review some recent results on global bifurcation of limit cycles, steady states in general predator-prey models, some with spatial structure, and some with strong Allee effect on the prey population. These results help to explain the rich spatial-temporal patterns which the system possesses.

**George A. Elliott**

University of Toronto

Colloquium

3:00 PM, December 10, 2009

HH-3017*"The classification problem for amenable C*-algebras*"

No Abstract

**Dr. Ronald Haynes**

Department of Mathematics and Statistics, Memorial University

Applied Dynamical Systems Seminar

1:00 PM, December 4, 2009

HH-3017*"Moving Meshes, Domain Decomposition and Other Initiatives*"This talk will review my current research directions in the design,analysis and implementation of numerical methods for differential equations. In particular, we will consider aspects of adaptive methods for PDEs including moving mesh, h-refinement and multi-rate methods; as well as natural marriages between these approaches and domain decomposition for parallel implementation. Along the way I will identify problems of (hopefully) mutual interest with the dynamical systems community with the hope of forging collaboration and student co-supervision.

**Dr. Tomas Liko**

Memorial University and Penn. State University

Departmental Seminar

1:00 PM, November 16, 2009

HH-3017*"Isolated Horizons in String Theory and Particle Physics"*

Many problems arise when studying aspects of black holes by employing global techniques. For physically realistic situations, alternative quasilocal techniques must be employed to overcome the problems. We give an overview of one such quasilocal generalization, known as the isolated horizon framework, and specifically discuss its application to string theory and to particle physics.

**Dr. J.C. Loredo-Osti**

Department of Mathematics and Statistics, Memorial University

Combinatorics Seminar

2:00 PM, November 4, 2009

SN-3058*"Trees of descent, Steiner trees and the computation of likelihood in complex genealogies"*

There is a large class of important problems in genetics for which all the data consist of one or very few large and complex pedigrees. Each pedigree can be seen as a realization of the genetic process. Although the pedigree may have many members, in general, from a genetic perspective, they are of little value as singletons. Thus, we are faced with the dilemma of carrying out the inference in situations where we cannot collect a large number of families but at most a handful of large pedigrees with marker/phenotype data recorded only for the individuals in most recent generations. Under these conditions the statistical modeling of genetic factors in the pedigree becomes crucial and the likelihood is the natural way to go. However, the computation of the exact likelihood of genetic linkage on large complex pedigrees is a daunting problem that challenges the full use of pedigree analysis. Some researchers resort to taking only one of the possible trees of descent into account to link known carriers of an allele to a common ancestor and do 'exact' computations on the selected subset. So the question would be 'does trimming the pedigree make sense?' and if so 'how the pedigree should be trimmed to retain the salient features of the genetic inheritance process?'. There is a connection between finding the most likely paths of descent of a genetic variant and reduction in pedigree complexity. Under a recessive-lethal mode of inheritance, maximum reduction in complexity is achieved by using a tree of minimal size (with the edge weights properly chosen), that is, a Steiner tree -a well known problem in graph theory-- and this solution can be seen as a constrained approximation to the solution to the paths of descent problem. These and related problems in a genetic linkage framework will be discussed in this presentation. This research is done in collaboration with Prof. K Morgan (McGill University) and CIHR and MITACS support.

**Dr. S.P. Singh**

Memorial University

Colloquium

1:00p.m., October 29, 2009

HH-3013*"Ky Fan's theorem and applications in nonlinear analysis."*

In this talk the best approximation theorem due to Ky Fan will be given. In brief its application to fixed point theory, best approximation and variational inequalities will be discussed. In the end, a result dealing with the convergence of approximating sequence will be presented where techniques of approximation theory will be used. A few results related to the convergence of iterative process will also be included.

**Dr. Daniel Horsley**

Department of Mathematics and Statistics, Memorial University

Combinatorics Seminar

2:00 PM, October 15, 2009

SN-3058*"Embedding partial Steiner triple systems"*

A partial Steiner triple system is said to be embedded in a complete Steiner triple system if the complete system can be obtained from the partial system by adding points and triples. In 1977 Lindner conjectured that every partial Steiner triple system of order $u$ has an embedding in a Steiner triple system of order $v$ if $v equiv 1,3 ({rm mod},}6)$ and $v geq 2u+1$. In this talk we discuss embeddings of partial Steiner triple systems and give an outline of the proof of Lindner's conjecture.

**Dr. Dariusz Dereniowski**

Algorithms and System Modeling Gdansk University of Technology

2:00 PM, October 8, 2009

SN-3058*Nonclassical measures for evaluating search strategies.*

In the (node or edge) searching problem a (simple or multi-) graph is given and the goal is to find a search strategy (a sequence of moves of the searchers) which leads to the situation with no contaminated vertices or edges in the graph. The optimization criterion considered mostly for such problems is the number of searchers required to clear a given graph. In this talk we discuss optimizing search strategies according to other measures, like cost or time.

**Dr. Keying Guan**

Beijing Jiaotong University

Departmental Colloquium

2:00 PM, September 21, 2009

HH-3017*"Exact Solution of the Plane Flow with Unsteady Vortex and Brownian Motion"*

Based on the conception "pseudo-potential" of the incompressible plane flow, an exact solution to the Euler equation is given. With the KAM theory and the second order Melnikov function, it is proved that this solution describes infinitely many unsteady vortices distributed periodically on the whole plane and the Brownian motion appears along the border region separating different vortices.

**Dr. Peixuan Weng**

South China Normal University Departmental Colloquium

2:00 PM, September 11, 2009*"Traveling Waves and Spreading Speeds for Evolutionary Systems"*

The asymptotic speed of propagation and traveling wave solutions are two important topics in the study of spatial dynamics of nonlinear evolutionary systems. In this talk, I will present a short survey on the recent progress and development about spreading speeds, minimal wave speeds, and traveling wave solutions of certain types of nonlinear evolutionary equations. I will also give an example to illustrate the application of the recently-developed theory of spreading speed and traveling wavefronts for monotone semiflows.