Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department News & Events

Department Colloquium - Florian Richter (Northwestern University)

Florian Richter (Northwestern University)

Friday, November 6th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Florian Richter (Northwestern University)

Title: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions.

Abstract: One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases. This naturally leads to a formulation of an extended form of Sarnak's Mobius randomness conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.

Florian Richter is a Boas Assistant Professor in the Department of Mathematics at Northwestern University. He received his Ph.D. from The Ohio State University in 2018 under the supervision of Vitaly Bergelson. He received The Elizabeth Clay Howald Presidential Fellowship and Louise B.C. Vetter award for excellence in research from Ohio State. He works on dynamical systems, combniatorics and number theory.

Department Colloquium - Emine Yildirim (Queen’s University)

Emine Yildirim (Queen’s University)

Friday, October 23rd, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Emine Yildirim (Queen’s University)

Title: Graphs and Combinatorics in Representation Theory of Algebras.

Abstract: Representation theorists of finite dimensional algebras often use quivers, also known as directed graphs, and many other combinatorial tools associated with these quivers. This is because we understand the module category of algebras via representation of quivers. On the other hand, we also capture the beautiful combinatorics of cluster algebras via the same representation theory. In this talk, I will outline how this machinery works along with some recent results on Cluster Categories we obtained joint with Charles Paquette using the combinatorics and representations theory of quivers.

Emine Yildirim is a Coleman Research Fellow within the Department of Mathematics and Statistics at Queen’s University. She obtained her Ph.D. in Mathematics from the Universite du Quebec a Montreal in 2018. She is mainly interested in representation theory of algebras, specifically path algebras, incidence algebras, and their representations. She also works on cluster algebras, their categorification and related combinatorics.

Department Colloquium - Rafael Potrie (U de la Republica-Uruguay)

Rafael Potrie (Universidad de la Republica-Uruguay)

Friday, October 16th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Rafael Potrie (Universidad de la Republica-Uruguay)

Title: Anosov flows and the fundamental group.

Abstract: The hairy ball theorem says that a vector field in the sphere must have some singularity. How does the dynamics interact with the topology of the underlying manifold in higher dimensions? We will discuss some instances of this question for dynamics in 3-manifolds, featuring a beautiful result due to Margulis and Plante-Thurston. Time permitting, we will touch upon more recent developments on the interactions between the topology and dynamics in 3 dimensions.

Rafael Potrie is an Associate Professor at the Universidad de la Republica-Uruguay. He obtained his Ph.D. in Mathematics from Universite Paris 13/Universidad de la Republica-Uruguay in 2012. He was an invited speaker of the Dynamical Systems session at the International Congress of Mathematicians (ICM) in 2018. His research mainly concerns the topological classification of partially hyperbolic systems in three-dimensional manifolds and its dynamical consequences. Other interests include smooth dynamics, ergodic theory, discrete subgroups of Lie groups, and the geometry of foliations and laminations.

Department Colloquium - Farouk Nathoo (University of Victoria)

Farouk Nathoo  (University of Victoria)

Friday, October 9th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Farouk Nathoo (University of Victoria)

Title: Spatial Statistical Modeling for Neuroimaging Data.

Abstract: I will describe three projects involving the analysis of neuroimaging data and the development of hierarchical spatial Bayesian models for each. In the first, we develop an approach for determining the location and dynamics of brain activity from combined magnetoencephalography and electroencephalography data. The resulting inverse problem is ill-posed and we propose a distributed solution based on a Bayesian spatial finite mixture model that incorporates the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states. In the second project, we consider statistical modelling of functional magnetic resonance imaging (fMRI) data which is challenging in part as the data are both spatially and temporally correlated. Motivated by an event‐related fMRI experiment, we propose a novel hierarchical Bayesian model with automatic selection of the auto‐regressive orders of the noise process that vary spatially over the brain. In the third project, we develop a Bayesian bivariate spatial model for multivariate regression analysis applicable to studies examining the influence of genetic variation on brain structure. Our model is motivated by an imaging genetics study of the Alzheimer's Disease Neuroimaging Initiative, where the objective is to examine the association between images of volumetric and cortical thickness values summarizing the structure of the brain as measured by magnetic resonance imaging (MRI) and a set of 486 SNPs from 33 Alzheimer's Disease (AD) candidate genes obtained from 632 subjects. A bivariate spatial process model is developed to accommodate the correlation structures typically seen in structural brain imaging data and we develop a mean-field variational Bayes algorithm and a Gibbs sampling algorithm to fit the model. We compare the new spatial model to an existing non-spatial model in our motivating application.

Department Colloquium - Elliot Paquette (McGill University)

Elliot Paquette (McGill University)

Friday, October 2nd, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Elliot Paquette (McGill University)

Title: Random perturbations of non-normal matrices.

Abstract: Suppose one wants to calculate the eigenvalues of a large, non-normal matrix. For example, consider the matrix which is 0 in most places except above the diagonal, where it is 1. The eigenvalues of this matrix are all 0. Similarly, if one conjugates this matrix, in exact arithmetic one would get all eigenvalues equal to 0. However, when one makes floating point errors, the eigenvalues of this matrix are dramatically different. One can model these errors as performing a small, random perturbation to the matrix. And, far from being random, the eigenvalues of this perturbed matrix nearly exactly equidistribute on the unit circle of the complex plane. This talk will give a probabilistic explanation of why this happens and discuss the general question: how does one predict the eigenvalues of a large, non-normal, randomly perturbed matrix?

Elliot Paquette is an Assistant Professor within the Department of Mathematics and Statistics at McGill University. He obtained his Ph.D.~in Mathematics from the University of Washington in 2013. He was an NSF Postdoctoral Fellow at the Weizmann Institute of Science from 2013-2016, and an Assistant Professor at the Ohio State University from 2016-2020. His research is in probability theory, with a focus on random matrix theory and on problems with geometric and topological inspirations.

Department Colloquium - Abdalrazzaq Zalloum (Queen's)

Abdalrazzaq Zalloum  (Queen's University)

Friday, September 25th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Abdalrazzaq Zalloum (Queen's University)

Title: Negative curvature in geometric group theory.

Abstract: Geometric group theory studies the interplay between the algebraic/combinatorial properties of infinite groups and the geometries of the spaces on which they act. A naive example of this phenomena is the following theorem: "An infinite group is free if and only if it admits a free action on some tree". In the previous theorem, the geometric property of the tree containing no loops informed the algebraic/combinatorial property of the group being free and vice versa; this is a theme in geometric group theory. A metric space $X$ is said to be hyperbolic if there exists a number $\delta$ such that for any geodesic triangle in $X$, the union of the {$\delta$-nbhd} of any two of its three sides contains the third, see the attached image. Group actions on hyperbolic spaces tend to be particularly informative. A fundamental (and almost defining) property of hyperbolic spaces is that infinite geodesics satisfy a \textit{local to global} property: to check whether an infinite path is a geodesic in $X$, you need only to check that in uniformly small windows. Given a nice action of an infinite group $G$ on a hyperbolic space $X$, Cannon showed that the local-to-global property of geodesics in $X$ is reflected in the combinatorial structure of $G$. In particular, he observed that the local-to-global property of $X$ is inherited by $G$ in the sense that all the combinatorial and growth information of the \textbf{infinite} group $G$ can be encoded using only a $\textbf{finite}$ amount of data: a finite graph. I will discuss recent work where we study groups acting on spaces satisfying a similar local-to-global property, and we will see the interplay between the geometric local-to-global properties of the space, and the combinatorial structure of the acting group. Some of the results I will discuss are joint with Cordes, Russell and Spriano.

Abdalrazzaq Zalloum is a Coleman post-doctoral fellow within the Department of Mathematics and Statistics at Queen's University, working with Thomas Barthelmé and Francesco Cellarosi. He obtained his Ph.D. in Mathematics from the SUNY Buffalo in 2019. He is mainly interested in geometric group theory, which studies the interplay between the algebraic structures of groups and the geometries of the spaces on which they act.

Department Colloquium - Serdar Yuksel (Queen's University)

Serdar Yuksel (Queen's University)

Friday, September 11th, 2020

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Serdar Yuksel (Queen's University)

Title: Geometry of Information Structures, Strategic Measures and Associated Control Topologies.

Abstract: In many areas of applied mathematics (including control theory, information theory, game theory) decentralization of information among several decision makers is unavoidable. Information and correlation structures determine who knows what information and how the decisions may be dependent leading to various problems on the geometry of correlation structures among decisions/controls. We define information structures, place various topologies on them, and study closedness and compactness properties on the (strategic) measures induced by decentralized control/decision policies under varying degrees of relaxations with regard to access to private or common randomness. Ultimately, we present existence and approximation results for optimal decision/control policies. We then discuss various upper and lower bounding techniques, through realizable and classically non-realizable (such as quantum correlations and non-signaling) convex relaxations and quantization. For each of these, we review or establish closedness and convexity properties and present a hierarchy of correlation structures. As a second main theme, we review or introduce various topologies on decision/control strategies defined independently from information structures, but for which information structures determine whether the topologies entail utility in arriving at existence, compactness, convexification or approximation results. These approaches, which we will term as the strategic measures approach (where the induced joint measure is considered) and the control topology approach (where a product space of individual control policy spaces is considered), lead to complementary results and solution methods in optimal stochastic control. (Joint work primarily with Prof. Naci Saldi, other collaborators will also be acknowledged).

Congratulations to Math & Stats graduating student Claire Smith

Claire Smith

July 13th, 2020

Claire graduated with BIMA-P-BSH -- Biology and Mathematics-Specialization – Bachelor of Science (Honours).

Medal in Mathematics and Statistics - Awarded to a graduating student who has demonstrated academic excellence in an honours degree who is deemed by a Department to have achieved the highest standing in a Plan offered by that Department. 

The Irene MacRae Prize in Mathematics and Statistics - Established by Margaret Crain in memory of Irene MacAllister MacRae, Arts '14, who was vice-president of the Mathematical Club while at Queen's.  Awarded at graduation to the departmental medalist in the Faculty of Arts and Science.


Congratulations to graduating MTHE students who received awards

Monday, July 6th, 2020

Congratulations to graduating Mathematics and Engineering (MTHE) students who received awards in 2020. 

University Medal in Mathematics and Engineering - awarded to a student who has the highest Grade Point Average for all courses of third and fourth years, provided the GPA is 3.5 or higher - Richard Linsdell

Annie Bentley Lillie Prize in Mathematics - awarded to the graduating student in the program of Mathematics and Engineering who has the highest average on courses in Mathematics in final year - Jonathan Bryan

Richard Linsdell

Richard Linsdell

Jonathan Bryan

Jonathan Bryan

Jonathan Bryan

Jonathan Bryan with Abdol-Reza Mansouri,
Chair of Mathematics & Engineering


Congratulations Mathematics and Statistics 2020 Graduates

June 22nd, 2020

Recently I was wandering around downtown Kingston watching the pubs and restaurants opening their patios, the serving staff elegant in their black clothing and their masks, and I was thinking how much our lives had changed in the past months and how “normal” might never be the same again.

Certainly this graduation year has not been normal and you are in every sense stepping into a new world. I hope your time at Queen’s has prepared you to meet this world, and if it has, that is largely to your credit, to the many hours of hard work and imaginative thought you have put into your experience here. For that, you are to be hugely congratulated and these short videos will give us, your teachers, a chance to express that. Best of luck going forward!

Peter Taylor
Undergraduate Chair
Dept of Mathematics and Statistics.