Seminars

Friday, Jan 21

12:30-1:20

Cancelled

Cancelled

Friday, Feb 11

12:30-1:20

Cancelled

Cancelled

Friday, Mar 4

12:30-1:20

TBA

Details TBA

Friday, Mar 25

12:30-1:20

TBA

Details TBA

Fall 2021

Friday, Sept 24

12:30-1:20

Dr. Aasaimani Thamizhazhagan

Department of Mathematics and Statistics, University of Winnipeg

Title: On the structure of invertible elements in certain Fourier-Stieltjes algebras

Abstract: Let G be a locally compact group. The Fourier-Stieltjes B(G) is defined as a dual object to the measure algebra M(G) in a sense that generalizes Pontryagin duality from the theory of abelian locally compact groups. Hence there is natural expectation that properties of M(G) ought to be reflected in B(G). In this talk, we characterize the invertible elements of B(G) for certain non-abelian Lie groups G. This can be viewed as a dual result to Taylor's characterization of invertible elements in M(G) for abelian G and provides partial verification to a conjecture of Illie and Spronk.

Friday, Oct 22

12:30-1:20

Department of Mathematics and Statistics, University of Winnipeg

Title: Computer proofs of some combinatorial congruences

Abstract: The classical congruence result of Lucas (1878) for the binomial coefficients "n choose m" modulo a prime p shows that looking at the base-p representations of n and m is often an efficient way to determine divisibility properties of the binomial coefficients modulop. Many authors have studied divisibility properties of famous combinatorial sequences along these lines. For instance, Alter and Kubota (1971) studied the Catalan numbers modulo p. Deutsch and Sagan (2006) looked at the Motzkin numbers, central Delannoy numbers, Apery numbers, etc., mod p. Rowland and Yassawi (2015) and Rowland and Zeilberger (2014) used finite automata to describe congruence properties of these types of sequences. We show how to combine the method of Rowland and Zeilberger with the software Walnut, which can prove many properties of so-called "automatic sequences", to give very quick, fully automated proofs of some of these congruence properties.

Friday, Nov 12

12:30-1:20

Department of Pure Mathematics, University of Waterloo

Abstract: In this short and informal talk, I will discuss some of thelessons learned from my experiences as a Winnipeg undergraduate student and a Waterloo graduate student. Emphasis will be placed on the strengths of UWinnipeg and the unique opportunities it affords its students. This talk will be particularly interesting to third and fourth year undergraduate students who are considering graduate studies.

Friday, Dec 3

12:30-1:20

Dr. Julien Arino

Department of Mathematics, University of Manitoba

Title: Considerations about case importations in the context of COVID-19

Abstract: The spatio-temporal spread of infectious diseases between human jurisdictions can be viewed as the repetition of several process-es, namely, transportation, importation, amplification and exportation. These processes operate differently depending on the scale at which they are considered. Taking the example of the current COVID-19 cris-is, top-level national jurisdictions imported the infection quickly and have, for the most part, remained with the infection since. However, zooming in at the level of local jurisdictions, there have been many phases of importation and amplification followed by periods without any transmission. As a consequence, understanding the importation process, how to lower its probability of success and its overall contrib-ution to local infection is important. I will present data concerning this process, then will discuss models that were developed to represent the process as well as evaluate some measures taken to alleviate importa-tion risks.

Winter 2021

Friday, April 9

12:30-1:20

via Zoom

Dr. Zeinab Mashreghi

Department of Mathematics and Statistics, University of Winnipeg

Details TBA

Friday, March 19

12:30-1:20

via Zoom

Prof. Jim Stallard

Department of Mathematics and Statistics, University of Calgary

Details TBA

Friday, January 29

12:30-1:20

via Zoom

Dr. Melissa Huggan

Department of Mathematics, Ryerson University

Title: Combinatorial Game Theory

Abstract: Two player, perfect information games of no chance have beautiful mathematics underpinning their study. These are called combinatorial games. I will give a gentle introduction to combinatorial game theory. We will go on a journey via rulesets, including NIM, HACKENBUSH, and DOMINEERING, to illustrate several of the main theoretical results within this area of mathematics.

Fall 2020

Friday, December 4

12:30-1:20

via Zoom

Dr. Gyanendra Pokharel

Department of Mathematics and Statistics, University of Winnipeg

Title: Likelihood-based model classification and prediction of spatial epidemicsAbstract: In an emerging epidemic, public health officials must move quickly to control the spread. Information obtained from statistical disease transmission models often informs the development of control strategies. Inference procedures such as Bayesian Markov chain Monte Carlo (MCMC) allow researchers to estimate parameters of such models, but are computationally expensive. Pokharel and Deardon (2014) introduced an approach for inference on infectious disease data based on the idea of supervised statistical and machine learning method. Their method involves simulating epidemics from various infectious disease models, and using classifiers built from the epidemic curve-based summary statistic to predict which model were most likely to have generated observed epidemic curves. In this work, I propose to replace epidemic curve-based summary statistic by a likelihood-based summary statistic calculated over a design matrix constructed over the pre-defined parameter space. Then, thus built classifier is used to detect the disease transmission kernel and model parameters for the observed data. This approach may perform better than the epidemic curve-based classification approach assuming that the likelihood-based summary statistic provides better information to the model.

Friday, November 20

12:30-1:20

via Zoom

Dr. Shakhawat Hossain

Department of Mathematics and Statistics, University of Winnipeg

Title: An efficient estimation approach to joint modelling of longitudinal and survival data

Abstract: The joint models for longitudinal and survival data have recently received a significant amount of attention in medical and epidemiological studies. Joint models typically combine linear mixed effects models for repeated measurement data and Cox models for survival time. When we are jointly modelling the longitudinal and survival data, variable selection and efficient estimation of parameters are especially important for performing reliable statistical analyses, which are lacking in the literature. In this paper we discuss the pretest and shrinkage estimation methods for jointly modeling longitudinal data and survival time data, when some of the covariates in both longitudinal and survival components may not be relevant for predicting the individuals' survival times. In this situation, we fit two models: the full model that contains all the covariates and the subset model that contains a reduced number of covariates. We combine the full model estimators and the estimators that are restricted by a linear hypothesis to define pretest and shrinkage estimators. We provide their numerical mean squared errors (MSE) and relative MSE . We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimators is strictly less than that of the full model estimators. Our proposed methods are illustrated by extensive simulation studies and by a real-data example.

This is the joint work with Jody Krahn (U of Winnipeg) and Dr. Shahedul Khan (University of Saskatchewan).

Friday, November 13

12:30-1:20

via Zoom

Dr. Ortrud Oellermann

Department of Mathematics and Statistics, University of Winnipeg

Title: The threshold dimension and threshold strong dimension of a graph

Abstract: Let G be a connected graph and u,v and w vertices of G. Then w is said to resolve u and v if the distance from u to w does not equal the distance from v to w. If there is either a shortest u-w path that contains v or a shortest v-w path that contains u, then we say that w strongly resolves u and v. A set W of vertices of G is a resolving set (strong resolving set), if every pair of vertices of G is resolved (respectively, strongly resolved) by some vertex of W.  A smallest resolving set (strong resolving set) of a graph is called a basis (respectively, a strong basis) and its cardinality, the metric dimension (respectively, the strong dimension) of G. The threshold dimension (respectively, threshold strong dimension) of a graph G, is the smallest metric dimension (respectively, strong dimension) among all graphs having G as a spanning subgraph. Graphs that are not spanning subgraphs of graphs with smaller metric dimension (or smaller strong dimension) are irreducible relative to the metric dimension (respectively, strong dimension). We present geometric characterizations for both the threshold dimension and threshold strong dimension of a graph and demonstrate the utility of these characterizations. We highlight some similarities and differences between these two invariants and show that they are not equal. We describe several bounds for these two invariants and discuss the existence of irreducible structures of a given order and dimension (strong dimension).

[This is collaborative work of two research groups: Group 1: Lucas Mol, Matthew Murphy, Ortrud Oellermann; Group 2: Nadia Benakli, Novi Bong, Shonda Dueck, Linda Eroh, Beth Novick and Ortrud Oellermann.]

Winter 2020

Friday, March 13

12:30-1:20

3M62

Dr. Aynslie Hinds

Institute of Urban Studies, University of Winnipeg

Title: Applying Your Statistics Knowledge and Skills in the Non-Profit Sector

Abstract: In this talk, I will discuss how I am using my statistics knowledge and skills to support community organizations with their research, evaluation, and information needs. Additionally, I will describe how students can apply their knowledge and skills to do similar work in a volunteer capacity with the support of Community Hub - Information and Research Partnerships (CHIRP).

Friday, February 28

12:30-1:20

Room 1L11

Dr. Vida Dujmović

School of Computer Science and Electrical Engineering, University of Ottawa

CANCELLED

Title: Graph colourings

Abstract: Graphs are mathematical structures used to model networks that arise in all areas of human endeavour. Graph colouring is among the most studied and most applicable topics in graph theory.  In this talk, I will introduce several graph colouring problems, starting with the famous four colour theorem for colouring maps. I will then talk about a graph colouring problem that arises in the study of pattern-avoiding sequences. Finally, I will present a recent breakthrough at the intersection of the two previous topics, where colleagues and I solved a 20-year old open problem.

Friday, February 14

12:30-1:20

Room 3M62

Dr. Maxime Turgeon

Department of Statistics, University of Manitoba

Title: Principal Component of Explained Variance: an optimal and efficient dimension reduction method

Abstract: Recent technical advances in genomics and neuroimaging have led to an abundance of high dimensional and correlated data. In this context, dimension-reduction techniques can be used to summarize high-dimensional signals, to further test for association with the covariates of interest. We revisit one such approach, renamed here as Principal Component of Explained Variance (PCEV). This method seeks a linear combination of outcomes by maximising the proportion of variance explained by the covariates of interest. In the first half of this talk, we propose a general high-dimensional analytical framework that is conceptually simple and free of tuning parameters. We provide a computational strategy for high-dimensional outcomes that relies on an assumption of block-independence that is natural in the context of genomics and neuroimaging. We also investigate the robustness of our approach when this assumption is not met. In the second half, using random matrix theory, we propose an empirical estimator that provides a fast way to compute valid p-values to test the significance of a high-dimensional multivariate association. We illustrate these different concepts using DNA methylation data and neuroimaging data.

Friday, January 31

12:30-1:20

Room 2M74

Dr. Melody Ghahramani

Department of Mathematics and Statistics, University of Winnipeg

Title: Time series regression for zero-inflated and overdispersed count data: a functional response model approach

Abstract: Count time series data feature prominently in epidemiology, business, and environmental sciences. Often, such data exhibit zero-inflation and overdispersion in addition to serial dependence. Parametric models such as the zero-inflated negative binomial distribution are employed to account for zero-inflation and overdispersion. In practice, the conditional variance structure may be unknown or may not be negative binomial. In this talk, I develop a distribution-free approach for estimation of regression parameters of conditionally overdispersed and zero-inflated time series models. Model parameters are optimal in the Godambe-information sense. Simulation studies indicate that our method is robust to model misspecification with small relative bias and nearly the same efficiency as that of the MLE for some observation-driven count time series processes. A case study comparing our method with fully parametric methods using weekly syphilis counts from 2007--2010 in Virginia, USA illustrates the benefit of our method.

This is joint work with Scott White (UWinnipeg statistics major graduate).

Fall 2019

Friday, November 29

12:30-1:20

Room 2M67

Dr. Elif Acar

Department of Statistics, University of Manitoba

Title: Conditional dependence models under covariate measurement error

Abstract: In many applications, covariates are subject to measurement error. While there is a vast literature on measurement error problems in regression settings, very little is known about the impact of covariate measurement error on the dependence parameter estimation in multivariate models. In this work, we address the latter problem using a conditional copula model, and show that the dependence parameter estimates can be significantly biased if the covariate measurement error is ignored in the analysis. We identify the underlying bias pattern from the direction and magnitude of marginal effect sizes and introduce an analytical bias correction method for the special case of the Gaussian copula. For general conditional copula models, a likelihood-based correction method is proposed, in which the likelihood function is computed via Monte-Carlo integration. Numerical studies confirm that the proposed bias-correction methods achieve accurate estimation of the dependence parameter.

Monday, November 4

12:30-1:20

Room 1L12

Dr. Karen Kopcuik

Department of Cancer Epidemiology and Prevention Research, Alberta Health Services

Title: Research by statistics students? Really?

Abstract: Statisticians are critical in a growing number of fields because they can use data to answer complex questions and problems. With more amounts and types of data being collected, along with better technology, the demand for new ways to analyse data continues at a fast pace. The job prospects for statisticians and data scientists who can work with and analyse complex data and who can develop new methods is growing exponentially.

In this talk, I will describe exciting career opportunities in statistics. I will also describe several research projects carried out by my undergraduate, graduate and post-graduate students. These projects will show the technical and computational skills used by these students and how they develop with more educational training. These students made important research contribuations and their research experience helped them pursue graduate studies and get their dream jobs.

Monday, October 28

12:30-1:20

Room 3M64

Dr. Jessica Striker

Department of Mathematics, North Dakota State University

Title: Mind-boggling toggling

Abstract: The toggle group is a simply presented permutation group generated by certain involutions, called toggles. Despite its simple description, the toggle group turns out to be a powerful gadget for finding surprising connections between various objects, discovering intriguing dynamical phenomena, and proving results related to statistical physics. In this talk, we give a tour of the toggle group, with connections to algebra, geometry, combinatorics, and physics.

Friday, October 18

1:30-2:20

Room 2C13

Dr. Karen Yeats

Department of Combinatorics and Optimization, University of Waterloo

Title: Combinatorial approaches to an arithmetic graph invariant with applications in quantum field theory

Abstract: The c2 invariant is an arithmetic graph invariant defined in order to better understand Feynman integrals. I will introduce it and discuss the combinatorial and enumerative approach that I have recently been using to make progress in understanding it.

Friday, Sept 20

12:30-1:20

Room 3M64

Manitoba Hall

Dr. Lucas Mol

Department of Mathematics and Statistics, University of Winnipeg

Title: THE REPETITION THRESHOLD FOR BINARY RICH WORDS

Abstract: A word is a finite or infinite sequence of symbols taken from some finite alphabet. A square (or 2-power) is a word of the form xx, where x is a nonempty word (e.g., murmur). One can also define fractional powers; alfalfa is a 7/3-power, while edited is a 3/2-power. A palindrome is a finite word that reads the same forwards and backwards. A word of length n is called rich if it contains n nonempty palindromic factors. An infinite word is called rich if all of its finite factors are rich.

Pelantová and Starosta demonstrated that every infinite rich word contains a square as a factor. This raises the question - what powers can be avoided by infinite rich words? We give a complete (and surprisingly irrational) answer to this question over the binary alphabet.

Undergraduate students are encouraged to attend!

Winter 2019

Wednesday, February 27

12:30-1:20

Room 1L11Lockhart Hall

Dr. Jean-Marie De Koninck

Department of Mathematics and Statistics, Laval University, Québec City

Title: THE SECRET LIFE OF MATHEMATICS

Abstract: Your doctor tells you that you have tested positive for a serious disease and he also tells you the test is reliable in 98% of the cases; should you be worried?  Can math be useful in eliminating traffic jams? Why do airline companies practice overbooking and pretend that it is for your own good?  In soccer, how important is it to score the first goal? Why hockey coaches should pull their goalie much earlier than they usually do. These are some of the topics that illustrate the importance of mathematics in our daily lives and that Jean-Marie De Koninck will cover in his talk «The Secret Life of Mathematics».

Jean-Marie De Koninck has been a researcher and professor of mathematics at Université Laval for more than forty years and is well known to the scientific community for his work in analytic number theory. He is the author of 15 books and 150 peer reviewed articles in scientific journals. He is now Professor Emeritus. Professor De Koninck has also hosted his own science outreach television show "C'est mathématique!", broadcasted on the French-Canadian channel (Canal Z) and later on TFO (Télévision française de l'Ontario). In 2005, he created the Sciences and Mathematics in Action (SMAC) program whose purpose is to excite kids about science and mathematics. He is well known by the general public as the founder of Operation Red Nose, a road safety operation involving over 55,000 volunteers across Canada. He was also very active in the media during the ten years he acted as President of the Table québécoise de la sécurité routière. He is now a member of the Board for the Société de l'assurance automobile du Québec. Many have also seen him as a color-commentator for nationally televised swim events.

Wednesday,  January 30

12:30-1:20

Room 3M69

Dr. Mahmoud Torabi, Associate Professor of Bio/statistics, Department of Community Health Sciences, University of Manitoba

Title: Spatial Modeling of Disease Mapping: An Introduction

Abstract: In traditional statistics, we frequently assess the effects of exposure on health outcomes through regression analysis. Such analysis can take many forms: linear, Poisson, and logistic regression are perhaps the most familiar. The same models can be used in spatial analysis after we adapt them to incorporate our ideas about neighborhood relationships and spatially correlated error terms.

In this talk, I will review some basic regression models (normal and possibly non-normal data) assuming that the observations are independent from each other. I extend these basic models with relaxing the assumption of independent errors and study possible spatial pattern of error terms. I will show some real data analyses through the talk.

Fall 2018

Monday, Oct. 29 12:30

Room 1L12

Lockhart Hall

Dr. David Haziza

Department of Mathematics and Statistics, Université de Montréal

Title: AN INTRODUCTION TO ESTIMATION IN THE PRESENCE OF MISSING DATA

Abstract: Every time data are collected, it is virtually certain that one will face the problem of missing values. Missing data are common in clinical trials, where dropout or noncompliance may lead to missing responses for some subjects. Missing data also arise in surveys and in administrative files (e.g., medical records). Missing data are undesirable because they make survey estimates vulnerable to nonresponse bias. Estimation procedures based on observed cases only tend to be biased. Also, observing a portion of the data results in a loss of information, which ultimately can lead to point estimates with larger standard errors due to reduced sample size. In this talk, we will review the concepts of MCAR/MAR/NMAR and describe two approaches for dealing with missing data: weighting and imputation.

David Haziza is a Professor in the department of mathematics and statistics at Université de Montréal. His research interests include inference in the presence of missing data, resampling methods and robust estimation in the presence of influential units. He is a consultant at Statistics Canada where he spends one day per week. David has already received a number of awards in his career, including the 2018 CRMSSC prize in statistics and the 2018 Gertrude Cox Award. He is also a Fellow of the American Statistical Association.

Friday, Sept 28 12:30 Room 1L12

Dr. Erica Moodie, Department of Epidemiology, Biostatistics, & Occupational Health, McGill University

Title: An introduction to causal inference in statistics

Abstract: Statistical causal inference is a framework that is used to try to discover the structure of the data and eliminate any spurious explanations for an observed association. A particular challenge in causal inference is the issue of confounding, which arises in nonexperimental studies or when there is non-compliance in a randomized trial. In this seminar, I will give a brief history of causality and an introduction to some fundamental principles in causal inference in statistics.

Winter 2018

Monday, March 2612:30 to 1:20 pmRoom 1L11 Dr. Christian Léger, Université de Montréal

Title:  Statistics or How Making Sense of Data is the New Gold Rush!

Abstract:  Data are everywhere in our lives. Their abundance is sometimes breathtaking. But these nuggets are useless unless we can make sense of them. This is why statistician/data scientist often comes up on top of any survey of high paying, high demand jobs! In this lecture, I will give an overview of the importance of statistics. Through examples, we will see different areas where statistics plays a major role. We will also see the importance of bias and variance in uncovering meaning in the data. As the field is always evolving, some current research topics will also be presented.

Friday, March 1612:30 to 1:20 pmRoom 3M67 Manon Stipulanti, University of Liège

Title:  Pascal-like triangles: base $2$ and beyond

Abstract: The Pascal triangle and the corresponding Sierpi\'nski gasket are well-studied objects. They exhibit self-similarity features and have connections with dynamical systems, cellular automata, number theory and automatic sequences in combinatorics on words. The link between those two objects is well-known and can be understood in the following way. Consider the intersection of the lattice $\mathbb{N}^2$ with the region $[0,2^n]\times [0,2^n]$. Then the first $2^n$ rows and columns of the usual Pascal triangle $(\binom{m}{k}\bmod{2})_{m,k< 2^n}$ provide a coloring of this lattice: the square on the mth row and kth column is colored in white (resp.; black) if $\binom{m}{k} \equiv 0 \bmod{2}$ (resp.; $\binom{m}{k} \equiv 1 \bmod{2}$). If we normalize this compact set by a homothety of ratio $1/2^n$, we get a sequence of compact subsets of $[0,1]\times [0,1]$ converging, for the Hausdorff distance, to the Sierpi\'nski gasket when $n$ tends to infinity. In a work in collaboration with Julien Leroy and Michel Rigo (University of Liège), we extend this convergence to a generalized Pascal triangle by considering the binary expansions of integers and the binomial coefficients of finite words. More precisely, a finite word is simply a finite sequence of letters belonging to a finite set called the alphabet. In combinatorics on words, one can introduce the binomial coefficient $\binom{u}{v}$ of two finite words $u$ and $v$ which is the number of times v occurs as a subsequence of u (meaning as a scattered'' subword). This concept naturally extends the binomial coefficient of two integers. Related to this triangle P2, we also define the sequence $(S_2(n))_{n\ge 0}$ that counts the number of positive entries on each row of P2. This sequence exhibits a strong structure: it is palindromic between powers of 2. This suggests that it is 2-regular in the sense of Allouche and Shallit. Finally, its summatory function has a particular behavior that is worth studying in details. We also extend those results to the Zeckendorff numeration system using Fibonacci numbers and, more recently, to any Parry--Bertrand numeration system.

Wed, March 2112:30 to 1:20 pmRoom 1L07 Dr. Shakhawat Hossain

Title:  Shrinkage estimation method of exponentiated Weibull regression model for time-to-event data

Abstract: In this talk, we consider the exponentiated Weibull model, which includes as special cases the Weibull, log-logistic, and log-normal distributions.  This model is broadly used to model time-to-event data in many studies and the primary focus of this data is to find the relationship between the time-to-event and the covariates.   This leads to the regression model that may have many covariates, some of which may not be significantly related to the survival time.  In that we use some auxiliary or non-sample information on insignificant covariates in the unrestricted model to produce a restricted model.  The shrinkage estimators optimally combine the unrestricted and restricted model estimators and outperform the maximum likelihood estimator (MLE) under the quadratic loss.   Asymptotic properties of these estimators including biases and risks will be discussed. A simulation study is conducted to assess the performance of the proposed estimators with respect to the unrestricted MLE. This study will be incorporated with varying sample sizes, different hazard shapes, and percentages of censored observations.  Estimators will be compared based on bias, risk, and mean squared prediction error. The relevance of the proposed estimators will be illustrated with two real data sets.  This is joint work with Shahedul Khan, University of Saskatchewan.

Tuesday, March 64:00 pmRoom 1L11

Dr. Micah McCurdy

Calling all hockey fans

Ever wonder if a certain hockey player is hurting or helping your favourite hockey team?

Well, Micah McCurdy might be able to sort that out through math, data and statistics. McCurdy is a mathematician who makes pictures to try and help the public understand hockey. He will speak at UWinnipeg on Isolating Individual Player Threat in the NHL on Tuesday March 6, 2018 at 4:00 pm in Room 1L11, Lockhart Hall. McCurdy uses data to measure results about hockey that can also help you do the math for your team.

This lecture is free and open to the public and is part of the Math and Stats Lecture Series.

Title: Isolating Individual Player Threat in the NHL Abstract: To tease apart which players are helping their teams and which are hurting, we turn, perhaps predictably, to regression. Somewhat less predictably, we quantify our observations of team performance in a function space whose elements measure shot fluxes - rates of shot generation from a given location. This lets us capture an aspect of shot quality as well as shot quantity. We obtain estimates of individual player impact on 5v5 offence and defence, isolated from the impact of their teammates, their starting shift position on the ice, and the score environment in which they are deployed. Along the way, we obtain a possibly novel and definitely simple closed form for a certain combinatorial regression

“I intend to make all of my research available to the public, for free,” shares McCurdy. “I find working in this way to be immensely satisfying and I do not aspire to a team position, especially not if it requires removing my public work from the internet, as we have seen in a number of prominent cases.”

McCurdy lives in Halifax and is employed mostly by the public who subscribe to his website, hockeyviz.com He is also employed intermittently by Saint Mary’s University, where he teaches undergrads. He also works with NHL teams.

Fri, Feb 912:30 - 1:20 pmRoom 3M64

Title: Critical exponents of balanced words

Abstract: This talk is about two fundamental concepts in combinatorics on words: balance and repetition.  A word w is "balanced" if, for every pair u,v of subwords of w of the same length, and every letter a, the number of a's in u and v differ by at most 1.  We are interested in what kinds of repetitions are avoidable/unavoidable in such words.  We measure repetitions by their "exponent": the exponent of a word is the ratio of its length to its period.  Over a binary alphabet the class of infinite aperiodic balanced words is identical to the well-studied class of Sturmian words.  The repetitions in Sturmian words are well-understood.  In particular, there is a formula for the critical exponent (supremum of exponents e such that x^e is a subword for some word x) of a Sturmian word.  It is known that the Fibonacci word has the least critical exponent over all Sturmian words and this value is (5+sqrt(5))/2.  However, little is known about the critical exponents of balanced words over larger alphabets.  We show that the least critical exponent among ternary balanced words is 2+sqrt(2)/2 and we construct a balanced word over a four-letter alphabet with critical exponent (5+sqrt(5))/4.  This is joint work with J. Shallit and E. Vandomme.

Fall 2017

Tues, Dec. 5 1:30 pm - 2:45 pm Room 1L06 Dr. Mohammad Jafari Jozani Associate Professor, Department of Statistics, University of Manitoba

Title: Towards more efficient and less expensive follow up analysis of bone mineral density in large cohort studies

Abstract: We develop a new methodology for analyzing upper and/or lower quantiles of the distribution of bone mineral density using quantile regression. Nomination sampling designs are used to obtain more representative samples from the tails of the underlying distribution.  We propose new check functions to incorporate the rank information of nominated samples in the estimation process.  Also, we provide an alternative approach that translates estimation problems with nominated samples to corresponding problems under simple random sampling (SRS). Strategies are given to choose proper nomination sampling designs for a given population quantile.  We implement our results to a large cohort study in Manitoba to analyze quantiles of bone mineral density using available covariates. We show that in some cases, methods based on nomination sampling designs require about one tenth of the sample used in SRS to estimate the lower or upper tail conditional quantiles with comparable mean squared errors. This is a dramatic reduction in time and cost compared with the usual SRS approach.

This talk is based on a work in collaboration with Ayilara Olawale Fatai and Bill Leslie.

Fri, October 612:30 pm - 1:20 pmRoom 1L07 Dr. Vaclav Linek

Title: Tilings and Skolem Sequences

A Skolem sequence of order n is a sequence of the numbers 1, 2,……n each occurring twice, where the two occurrences of each number j are exactly j positions apart (so there are j - 1 symbols between the two j’s). Thus, S = 4, 1, 1, 3, 4, 2, 3, 2 is a Skolem sequence of order 4: the 1s are one position apart, the 2s are two positions apart, the 3s are three positions apart, and the 4s are four positions apart. Similarly, S = 3, 4, 5, 3, 2, 4, 2, 5, 1, 1 is a Skolem sequence of order 5, and S = 1, 1, 3, 4, _ , 3, 2, 4, 2 is a variant: a split Skolem sequence of order 4 with a hole in the middle. Skolem sequences are used to construct combinatorial designs and are of interest on their own. Many parametrized families of these sequences have appeared over the years. We will give a unifying conceptual treatment of these parametrizations as tilings. (Joint work with B. Stevens and S. Mor).

Winter 2017

Wed, April 1212:30 pm - 1:20 pmROOM 2M77 Dr. Scott RodneyAssociate 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 EzzatDept. of Mathematics and StatisticsUniversity 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 PMCarol Shields Auditorium, 2nd floor of the Millennium Library Sohail KhanDept. of Mathematics and StatisticsUniversity 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 1512:30 - 1:20Room 1L04, Lockhart Hall,UWinnipeg Dr. Sanjoy SinhaSchool of Mathematics and StatisticsCarleton 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 1312:30 - 1:20Room 1L06, Lockhart Hall, UWinnipeg

Dr. Karen MeagherDept. 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. 212:30 - 1:20Room 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. 1812:30 - 1:20Room 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 412:30 - 1:20 pmRoom 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 2112:30 - 1:20 pmRoom 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 2812:30 - 1:20 pmRoom 2M74 Manitoba Hall Statistics Canada Information Session

Have you considered a career where you could…

• Develop your technical, analytical and managerial skills in a stimulating and professional environment;
• Benefit from a training and development program with varied assignments; and
• Have excellent prospects for advancement?

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 1812:30 - 1:20 pmRoom 1L07 Dr. Brett Stevens, ProfessorSchool of Mathematics and StatisticsCarleton 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 2612:30 - 1:20 pmRoom 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 312:30 - 1:20pmRoom 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 612:30 to 1:20Room 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 1812:30 to 1:20Room 1L04 Michael Pawliuk

Former U of W Honours student in MathematicsPhD Candidate, University of Toronto

ABSTRACT:

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

SEMINAR MOVED TO JANUARY 2016

changed to December 412:30 to 1:20Room 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

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 amRoom 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.