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.

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.

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.

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.

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.