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Seminars

Seminars and Talks


Winter 2017

Wed, April 12
12:30 pm - 1:20 pm
ROOM 2M77
Dr. Scott Rodney
Associate Professor,
Department of Mathematics, Physics and Geology,
Cape Breton University

Title: Poincare's Inequality and Neumann Problems

Recently, my group has devoted much time to the development of an axiomatic framework that gives continuity of weak solutions to a large class of quasilinear PDE in divergence form with rough coefficients.  In this talk I will begin with a general discussion of sufficient conditions.  I will then focus on a new result giving an equivalence between the validity of a weighted Poincar\'e inequality and the existence of a weak solution to a Neumann problem for a matrix weighted $p$-Laplacian.  That is, for $1\leq p<\infty$ and a $p/2$-integrable $n\times n$-valued matrix function $Q(x)$ on a bounded open subset $E$ of $\mathbb{R}^n$, we will consider weak solutions of \Delta_p u = \sqrt{Q(x)}\nabla u(x)^{p-2}Q(x)\nabla u(x)= f(x)|^{p-2}f(x) in $E$ where $f$ is assumed to belong only to a weighted $L^p$ class.

Friday, March 17

12:30 pm – 1:20 pm

Room 1C16A

Dr. Shannon Ezzat
Dept. of Mathematics and Statistics
University of Winnipeg

Title:  Pi

Most students know the mathematical fact that pi cannot be expressed as a ratio of whole numbers. However, very few students know why this fact is true. We will show why this well-known result is indeed true using a proof by contradiction.

Wednesday March 8th, 12:10 - 12:50 PM
Carol Shields Auditorium, 2nd floor of the Millennium Library
Sohail Khan
Dept. of Mathematics and Statistics
University of Winnipeg

Title:  “Let’s Quantify the Chances: Probability Theory and Its More Practical Uses”

http://wpl.winnipeg.ca/library/pdfs/posters/skywalkwinter2017.pdf

Wed., March 15
12:30 - 1:20
Room 1L04, Lockhart Hall,
UWinnipeg
Dr. Sanjoy Sinha
School of Mathematics and Statistics
Carleton University

Title: Joint modeling of longitudinal and time-to-event data

Abstract:

In many clinical studies, subjects are measured repeatedly over a fixed period of time. Longitudinal measurements from a given subject are naturally correlated. Linear and generalized linear mixed models are widely used for modeling the dependence among longitudinal outcomes. In addition to the longitudinal data, we often collect time-to-event data (e.g., recurrence time of a tumor) from the subjects. When multiple outcomes are observed from a given subject with a clear dependence among the outcomes, a natural way of analyzing these outcomes and their associations would be the use of a joint model. I will discuss a likelihood approach for jointly analyzing the longitudinal and time-to-event data. The method is useful for dealing with left-censored covariates often observed in clinical studies due to the limit of detection. The finite-sample properties of the proposed estimators will be discussed using results from a Monte Carlo study. An application of the proposed method will be presented using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis (GenIMS) study.

Friday, January 13
12:30 - 1:20
Room 1L06, Lockhart Hall, UWinnipeg

Dr. Karen Meagher
Dept. of Mathematics and Statistics, University of Regina

TITLE: “Cocliques in Derangement Graphs”

Abstract: 

The derangement graph for a group is a Cayley graph for a group G with connection set the set of all derangements in G (these are the elements with no fixed points).  The eigenvalues of the derangement graph can be calculated using the irreducible  characters of the group. The eigenvalues can give information about the graph, I am particularly interested in applying Hoffman's ratio bound to bound the size of the cocliques in the derangment graph. This bound can also be used to obtain information about the structure of the maximum cocliques. I will present a few conjectures about the structure of the cocliques, this work is attempting to find a version of the Erdos-Ko-Rado theorem for permutations. 

Fall 2016

Friday, Dec. 2
12:30 - 1:20
Room 2C13, Centennial Hall, UWinnipeg
Dr. Anna Stokke

Title:  Lattice path proofs for Jacobi-Trudi formulas

Abstract:  

Schur functions, which play an important role in symmetric function theory and in the representation theory of the general linear group, can be defined in terms of semistandard Young tableaux.  The Jacobi-Trudi identity expresses a Schur function as a determinant involving certain homogeneous symmetric functions.  Gessel and Viennot gave a proof of the Jacobi-Trudi identity using non-intersecting lattice paths.  I will discuss Gessel and Viennot's proof as well as new proofs for symplectic and orthosymplectic Jacobi-Trudi identities.

This talk will be accessible to undergraduate students in mathematics.

Friday, Nov. 18
12:30 - 1:20
Room 2C13, Centennial Hall, UWinnipeg
Jeff Babb Title: Multivariate statistical analysis: using R software to assess multivariate normality and to draw inferences based upon Hotelling’s T2 statistic

Abstract:

Many inference procedures in multivariate statistical analysis are based upon the multivariate normal (MVN) distribution and Hotelling’s T2 statistic.  This talk will discuss the multivariate normal distribution, outline an approach for assessing multivariate normality, and examine procedures which utilize Hotelling’s T2 statistic to draw inferences about a mean vector and the difference in mean vectors.  Examples using R software will be provided. 

Friday, November 4
12:30 - 1:20 pm
Room 2C13, Centennial Hall, UWinnipeg
Dr. Lucas Mol

Title: A family of patterns with reversal with interesting avoidance properties

Abstract:

A pattern p is a word over letters called variables. An instance of p is the image of p under some nonerasing morphism. A word w is said to avoid p if it contains no instance of p. A pattern p is called k-avoidable if there are infinitely many words over an alphabet of size k that avoid p. We say that p is avoidable if it is k-avoidable for some k and unavoidable otherwise. The avoidability index of an avoidable pattern p is the least number k such that p is k-avoidable. The question of whether there are avoidable patterns of index greater than 5 remains open. Additionally, there are relatively few known examples of patterns of index 4 or 5, and all known examples are quite long and complex.

Recently, work has been done on patterns with reversal, in which the reversal or mirror image of variables is allowed. An instance of a pattern with reversal p is the image of p under some nonerasing morphism which respects this reversal. The avoidability index of patterns with reversal is then defined as above for patterns. We present an infinite family of patterns with reversal whose avoidability indices are bounded between 4 and 5. These patterns with reversal are much simpler than the previously known patterns of index 4 or 5.

Friday, October 21
12:30 - 1:20 pm
Room 2C13, Centennial Hall, UWinnipeg
Dr. Narad Rampersad

Title:  Decidable properties of automatic sequences

Abstract:  

A k-automatic sequence is a sequence (of integers or just symbols) that can be generated by a finite automaton in the following sense:

Each state of the automaton has an associated output and the n-th term of the sequence is obtained as the output of the state reached by the automaton after reading the digits of n written in base k.  The prototypical example is the 2-automatic Thue-Morse sequence, whose n-th term is equal to the sum of the binary digits of n modulo 2.

Some classical work of Buchi gives an equivalent definition of k-automatic sequences in terms of a certain extension of Presburger arithmetic.  This extension remains decidable and in recent years many researchers (notably Shallit) have used the decidability of this theory to give entirely computerized proofs of many combinatorial properties of automatic sequences.  For instance, a classical combinatorial property of the Thue-Morse sequence is that it does not contain the same sequence of terms three times in a row.  This is an example of a combinatorial property that is provable by these automated techniques.  We give a survey of this approach and mention some recent new results that have been proven by means of such techniques.

Wednesday, September 28
12:30 - 1:20 pm
Room 2M74 Manitoba Hall
Statistics Canada Information Session

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  • Develop your technical, analytical and managerial skills in a stimulating and professional environment;
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 To find out more…

For additional information on opportunities for employment as a mathematical statistician with Statistics Canada, you can consult our recruitment web site at www.statcan.gc.ca/MArecruitment or contact us by e-mail at statcan.ma-recruitment-ma-recrutement.statcan@canada.ca.

How to apply…

Apply online at http://jobs.gc.ca (from September 21st to October 13th)

Winter 2016

Friday, March 18
12:30 - 1:20 pm
Room 1L07
Dr. Brett Stevens, Professor
School of Mathematics and Statistics
Carleton University

Title: Constructing covering arrays from the unions of hypergraphs

Abstract:  

Covering arrays are generalizations of orthogonal arrays which have applications to reliability testing.  Since repetition of coverage is permitted, one common method of construction is to vertically concatenate arrays until all $t$-tuples of columns are covered.  This corresponds to taking the union of several hypergraphs to produce a complete $t$-uniform hypergraph.  We survey constructions of this form.  We start with the Roux-type constructions. Then we examine arrays created from linear feedback shift registers.  In the case of strength 3 this construction is equivalent to showing that the union of the projective linear independence hypergraph and one isomorphic image of itself is the complete 3-uniform hypergraph.  We also show some examples of this method for higher strength. We close with a family of hypergraphs constructed from ordered orthogonal arrays (t,m,s-nets) that may be useful to consider for this construction method and ask if the union of two or more isomorphic copies yields a complete hypergraph.

Friday, February 26
12:30 - 1:20 pm
Room 3M59

Dr. Mostafa Nasri

Title: Equilibrium Problems: Solution Techniques and Applications

The main topic of this talk is to introduce the equilibrium problem in the context of optimization and its certain properties. The equilibrium problem provides a unified framework for a large family of problems such as complementarity problems, fixed point problems, minimization problems, Nash games, variational inequality problems and vector minimization problems. Although a large number of solution algorithms have been developed for this problem, there is still a wide scope for improvement and a need for extensive additional research in this realm. In particular, efficient and convergent algorithms for solving such problems are still being sought. With above motivations, proximal point algorithms are proposed for solving the equilibrium problem and their convergence properties are studied. Considering these proximal point algorithms, computer-amenable algorithms, called augmented Lagrangian algorithms, are developed for solving the same problem whose feasible sets are defined by convex inequalities. It is also shown that these algorithms can be extended to Banach spaces. Moreover, real-world problems are addressed for which the presented algorithms are applicable.

Wed., February 3
12:30 - 1:20pm
Room 2C15

Max Bennett

Title: How to count braids

In this talk I will introduce braids and cover a few interesting combinatorial properties that they exhibit, including an enumeration result of Albenque and Nadeau. Examining this leads to a solution to the word problem on braids. 

Very little prerequisite knowledge is necessary, but some familiarity with group theory would help.

2015

NOVEMBER

November 6
12:30 to 1:20
Room 1L06

Dr. Shakhawat Hossain

SHRINKAGE ESTIMATION FOR GENERALIZED LINEAR MIXED MODELS


In this paper, we consider the pretest, shrinkage, and penalty estimation procedures in the generalized linear mixed model when it is conjectured that some of the regression parameters are restricted to a linear subspace. We develop the statistical properties of the pretest and shrinkage estimation methods, which include asymptotic distributional biases and risks. We show that the pretest and shrinkage estimators have a significantly higher relative efficiency than the classical estimator. Furthermore, we consider the penalty estimator: LASSO (Least Absolute Shrinkage and Selection Operator), and numerically compare its relative performance with that of the other estimators. A series of Monte Carlo simulation experiments are conducted with different combinations of inactive predictors and the performance of each estimator is evaluated in terms of the simulated mean squared error. The study shows that the shrinkage and pretest estimators are comparable to the LASSO estimator when the number of inactive predictors in the model is relatively large. The estimators under consideration are applied to a real data set to illustrate the usefulness of the procedures in practice.
This is joint work with Trevor Thompson.

Wednesday, November 18
12:30 to 1:20
Room 1L04
Michael Pawliuk

Former U of W Honours student in Mathematics
PhD Candidate, University of Toronto

ABSTRACT:

In 1992, Hrushovski gave a positive answer the following
question: "If the enemy gives you a finite graph G, and an
isomorphism f of two of its induced subgraphs, is there a
larger finite graph G' that contains G and for which f
extends to an automorphism on all of G'?" This has
consequences for amenability of the automorphism group
of the countably infinite random graph.
The question is still interesting if you replace the word
"graph" with "metric space", "tournament" or "complete npartite
directed graph". We will present a construction due
to Mackey in the 1960s, that we adapted to give a positive
answer to question of Hrushovski for tournaments, and
many other classes of directed graphs.
This is joint work with Marcin Sabok (McGill).

SEMINAR MOVED TO JANUARY 2016

changed to December 4
12:30 to 1:20
Room 1L06

Dr. Ortrud Oellermann

PROGRESS ON THE OBERLY-SUMNER CONJECTURE


For a given graph property P we say a graph G is locally P if the open neighbourhood of every vertex induces a graph that has property P. Oberly and Sumner (1979) conjectured that every connected, locally k-connected, K_{1,k+2}-free graph of order at least 3 is hamiltonian. They proved their conjecture for k=1, but it has not been settled for any k at least 2. We define a graph to be k-P_3-connected if for any pair of nonadjacent vertices u and v there exist at least k distinct u-v paths of order 3 each. We make progress toward proving the Oberly-Sumner conjecture by showing that every connected, locally k-P_3-connected, K_{1,k+2}-free graph of order at least 3 is hamiltonian and, in fact, fully cycle extendable.

This is joint work with S. van Aardt, M. Frick, J. Dunbar and J.P. de Wet.

OCTOBER

Friday, October 23 

12:30 to 1:20

Room 1L06

Dr. James Currie

Binary patterns with reversal 

The study of words avoiding patterns is a major theme in combinatorics on words, explored by Thue and others. The reversal map is also a basic notion in combinatorics on words, and it is therefore natural that recently work has been done on patterns with reversals. Shallit recently asked whether the number of binary words avoiding xxx^R grows polynomially with length, or exponentially. The surprising answer (by C. and Rampersad) is `Neither`. As Adamczewski has observed, this implies that the language of binary words avoiding xxx^R is not context-free - a result which has so far resisted proof by standard methods.

Basic questions about patterns with reversal have not yet been addressed. In this talk, we completely characterize the k-avoidability of an arbitrary binary pattern with reversal. This is a direct (and natural) generalization of the work of Cassaigne characterizing k-avoidability for binary patterns without reversal, and involves a blend of classical results and new constructions.

This is joint work with Philip Lafrance.

Wednesday, Oct 7

12:30 to 1:20

Room 1L06

Bryan Penfound

Connecting the High School Pre-calculus Curriculum with Higher Education

Recently Bryan has developed an online pre-calculus review workshop for first-year students entering Calculus at the University of Winnipeg. The online workshop is divided into five main content areas, each with several online videos, problem sets, and diagnostic quizzes. The purpose of this session is to connect with high school pre-calculus teachers and to encourage the use of the online workshop as a student and teacher reference.

Friday, October 2

12:30 to 1:20

Room 1L06

Dr. Narad Rampersad

The Tarry-Escott Problem

The Tarry-Escott Problem is the following:  Given a "degree" k, find two distinct lists of integers {a_1,...,a_s} and {b_1,...,b_s} that satisfy

a_1 + a_2 + . . . + a_s = b_1 + b_2 + . . . + b_s

a_1^2 + a_2^2 + . . . + a_s^2 = b_1^2 + b_2^2 + . . . + b_s^2 .

.

.

a_1^k + a_2^k + . . . + a_s^k = b_1^k + b_2^k + . . . + b_s^k.

 

In 1851 Prouhet gave a solution for all k that requires lists of length 2^k.  By a counting argument one can show (non-constructively) that there is a solution using lists of size only k(k+1)/2+1, but the numbers are (potentially) huge.  Suppose we restrict the a_i and b_i to be in {1,...,m}.  Borwein, Erdelyi, and Kos showed that there is no solution for degree k > 16/7sqrt{m}+5.  The goal of the talk is to give the proof of this result.  Remarkably, this bound implies (by a non-trivial argument) the following result on words:  Any word of length m is uniquely determined by the multiset of its (scattered) subsequences of length at most floor(16/7sqrt{m}+5).

Thursday, June 4 10:00 to 11:30 am
Room 3C14

 

Jeff Babb, Department of Mathematics and Statistics, University of Winnipeg

Continuing Colloquium Series on R Software

ABSTRACT: Cluster analysis and minimum spanning trees are useful techniques for exploring multivariate data and assessing ways to group multivariate observations.  This talk will consider distance measures, four agglomerative hierarchical clustering methods (single linkage, complete linkage, average linkage, Ward linkage), related graphics and diagnostics (dendrogram, cophenetic matrix, cophenetic correlation), and minimum spanning trees.  Examples of using R statistical software for performing cluster analysis and obtaining a minimum spanning tree will be provided. 

Friday, February 6, 12:30 - 1:20pm Room 4C84 Robert Borgersen, Department of Mathematics, University of Manitoba TITLE: Progress Towards a Mathematics Placement Test at the University of Manitoba

ABSTRACT: A mathematics placement test is, in general, a test that attempts to measure a student's current competence in a number of mathematical abilities, and based on their current skills ''place'' them into only those classes for which they achieve a minimum level in all of the prerequisite abilities. The goal is to catch students who require remediation before they waste resources on a course they are not ready for. In this talk, I will discuss recent progress towards developing such a test at the University of Manitoba, opportunities such a test could provide, promising results we have had, and challenges we see on the horizon. There will be time for those in attendance to provide their thoughts, input, and opinions on the project.

Friday, February 27 12:30
Room 4M47 Theatre B

Dr. Jeffrey Rosenthal, Department of Statistics, University of Toronto

TITLE: "From Lotteries to Polls to Monte Carlo"

ABSTRACT: This talk will use randomness and probability to answer such questions as: Just how unlikely is it to win the lottery jackpot? If you flip 100 coins, how close will the number of heads be to 50? How many dying patients must be saved to show that a new medical drug is effective? Why do strange coincidences occur so often? If a poll samples 1,000 people, how accurate are the results? How did statistics help to expose the Ontario Lottery Retailer Scandal? If two babies die in the same family without apparent cause, should the parents be convicted of murder? Why do casinos always make money, even though gamblers sometimes win and sometimes lose? And how is all of this related to Monte Carlo Algorithms, an extremely popular and effective method for scientific computing? No mathematical background is required to attend. Jeffrey Rosenthal is an award-winning professor in the Department of Statistics at the University of Toronto. He received his BSc from the University of Toronto at the age of 20, and his PhD in Mathematics from Harvard University at the age of 24. His book for the general public, Struck by Lightning: The Curious World of Probabilities, was published in sixteen editions and ten languages, and was a bestseller in Canada. This led to numerous media and public appearances, and to his work exposing the Ontario lottery retailer scandal. Dr. Rosenthal has also dabbled as a computer game programmer, musical performer, and improvisational comedy performer, and is fluent in French. His web site is www.probability.ca

Friday, January 16 12:30
Room 3C30
Dr. Karen Gunderson Heilbronn Institute for Mathematical Research, University of Bristol TITLE: "Friendship hypergraphs"

ABSTRACT: For $r \ge 2$, an $r$-uniform hypergraph is called a \emph{friendship $r$-hypergraph} if every set $R$ of $r$ vertices has a unique `friend' - a vertex $x \notin R$ with the property that for each subset $A \subseteq R$ of size $r-1$, the set $A \cup \{x\}$ is a hyperedge. In the case $r = 2$, the Friendship Theorem of Erd\H{o}s, R\'{e}nyi and S\'{o}s states that the only friendship graphs are `windmills'; a graph consisting of triangles with a single common vertex. For $r \geq 3$, there exist infinite classes of friendship $r$-hypergraphs, not necessarily uniquely defined. These types of hypergraphs belong to a family that generalises the notion of a Steiner system, since in an $r$-uniform Steiner system, every set of $r-1$ vertices has a unique friend. In this talk, I shall give some background on these types of hypergraphs and describe new results on both upper and lower bounds on the size of friendship hypergraphs. Joint work with Natasha Morrison (Oxford) and Jason Semeraro (Bristol).

2014 Seminars
Monday, November 17 12:30
Room 3M64

Dr. Ortrud Oellermann,
The University of Winnipeg

TITLE: "Reconstruction Problems in Graphs"

ABSTRACT:    We say that a graph can be reconstructed from partial information about its structure if the graph can be uniquely determined from this information. We begin by giving an overview of graph reconstruction problems. In the second part of the talk we consider the problem of reconstructing a graph from its digitally convex sets; where a set of vertices S is digitally convex if every vertex, whose closed neighbourhood is contained in S, also belongs to S. (New results are joint work with P. Lafrance and T. Pressey)

     
Monday, Oct 27 12:30  3M64 Trevor Thomson
NSERC Summer Research Student
TITLE:  Efficient Estimation for Time Series Following GLMs

ABSTRACT:  In this talk, I will discuss the shrinkage and pretest estimation methods for time series of a generalized linear model with binary or count data when it is conjectured that some of the regression parameters may be reduced to a subspace. Especially, I examine these estimators for possible improvements in estimation and forecasting when there are many predictors in the linear models. The statistical properties of the pretest and shrinkage estimators including asymptotic distributional biases and risks are developed. They show that the shrinkage estimators have a significantly higher relative efficiency than the maximum partial likelihood estimator if the shrinkage dimension exceeds two and risk of the pretest estimator depends on the validity of the subspace of associated parameters.   A Monte Carlo simulation experiment is conducted for different combinations of inactive covariates and the performance of each estimator is evaluated in terms of the simulated relative mean squared error. The proposed methods are applied to a real data set to illustrate the usefulness of the procedures in practice.

 

     
Friday, April 25 12:30pm in Room 3M60 Dr. Azer Akhmedov
Mathematics Department, North Dakota State University
TITLE: “On the Hamiltonicity of Some Vertex Transitive Graph”
ABSTRACT: Lovasz has conjectured that every vertex transitive graph contains a Hamiltonian path. Another version of this conjecture states that every vertex transitive graph is Hamiltonian (contains a Hamiltonian cycle) unless it is isomorphic to one of the following 5 graphs: the complete graph K_2, the Petersen graph, the Coxeter graph, and two other graphs obtained from the Petersen and Coxeter graphs by truncation. 
 
Lovasz's Conjecture is wide open. A weaker Kneser conjecture states that a certain class of vertex transitive graphs are Hamiltonian. This claim has been verified in some special but significant cases (by Ya-Chen and Furedi), although in its full version, the conjecture is still open.
 
The Hamiltonicity problem of graphs turns out to be interesting also in musical theory as a way of generating musical morphologies. We have studied the Hamiltonicity problem for several graphs which are interesting to musical theorists. Some of these graphs are vertex transitive, and some are closely related to Kneser graphs. In the talk, I'll present a brief introduction to Hamiltonian graphs and mention several popular Hamiltonicity problems in graph theory. Then I'll discuss major ideas of the proof. This is a joint work with composer Michael Winter.
     
Friday, March 14 in 1L11 - 12:30-1:20 Dr. Randall Pyke
Department of Mathematics
Simon Fraser University
Fractals: A New (and Better) Way of Looking at the World.
Fractals are complicated geometric shapes that have captured the imagination of mathematicians for years, and more recently the larger public. It was the pioneering work of the mathematician Benoit Mandelbrot, beginning in the 1970's, that brought fractal geometry out from the remote corners of abstract mathematics into the mainstream. In this talk we will discuss what fractals are, how they are created, and some of their applications in areas outside of mathematics. We will also drift into the Julia and Mandelbrots sets.

 

Friday, March 14 in 2C13 10:30-11:20 Dr. Randall Pyke
Department of Mathematics
Simon Fraser University
FACULTY PRESENTATION

The Dynamics of Solitons

Solitons are localized solutions of nonlinear wave equations and appear in many applicable areas. Trying to understand their remarkable properties (robustness) have led to major advances in the theory of nonlinear partial differential equations and to their uses in areas such as solid-state electronics and nonlinear optics. I will introduce solitons and their close relatives, solitary waves, with examples, numerical experiments, and illustrate some methods for studying them.

 

Thursday , March 13 in 3M69 2:30-3:45 Dr. Randall Pyke
Department of Mathematics
Simon Fraser University
MATH/STAT & PHYSICS STUDENTS PRESENTATION

The Remarkable Theorem of Emmy Noether.

In 1918 Emmy Noether proved a theorem relating symmetries of a differential equation with conservation laws for solutions of the equation. It made precise what was up to then folklore in physics and is now the cornerstone in the modern theory of symmetries of differential equations. We will discuss this theorem by first introducing the calculus of variations, a powerful method in physics and differential equations and a major tool in modern analysis.
Wednesday February 5, 12:30pm in Room 4M46 Dr. Gerald Cliff, University of Alberta TITLE: “The groups of invertible and symplectic matrices ”

ABSTRACT:

I will first consider when a matrix can be inverted without switching rows. Then I will define symplectic matrices, which are somewhat analogous to orthogonal matrices. I will see which row switches are symplectic. This leads to the Weyl group of the symplectic group. I will assume the audience has no familiarity with symplectic matrices or Weyl groups.