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Algebra & Geometry Seminar

Monday, September 18th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 422

Speaker: Charles Paquette (RMC)

Title: The study of bricks in representation theory, and how they arose from cluster algebras.

Abstract: In this talk, I will discuss some of the implications that the theory of cluster algebras had in representation theory of finite dimensional algebras. In particular, it led to the study of some particular indecomposable modules. One such family is the set of bricks, where a brick is a module having a division ring as endomorphism ring. These modules also play a fundamental role in the study of geometric invariant theory for finite dimensional algebras, or in the study of torsion theory. Although important objects, there are still many open questions concerning bricks. My plan is to explore a few of those, from different perspectives, and provide some partial answers.

Number Theory Seminar

Tuesday, September 12th, 2023

Time: 3:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: M. Ram Murty (Queen's University)

Title: ARITHMETICAL FUNCTIONS OF SEVERAL VARIABLES

Abstract: We will survey several results in the theory of arithmetical functions of several variables, a subject that is not often treated in number theory textbooks though it should be!

Algebra & Geometry Seminar

Monday, September 11th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 422

Speaker: Sasha Zotine (Queen's University)

Title: Computing Higher Direct Images of Toric Morphisms

Abstract: Sheaf cohomology is a ubiquituous tool in algebraic geometry for understanding the structure of varieties---but how does one actually get one's hands on cohomology? In this talk, I will discuss computing sheaf cohomology (and higher direct images) of toric varieties, which translate geometry into combinatorics. This translation is far more accessible and amenable to computation, allowing us to get a more tangible grasp of the abstract constructions. In particular, I implemented an algorithm for computing the higher direct images of toric morphisms for line bundles in Macaulay2, which I will demonstrate.

Math & Stats Department Colloquium

Friday, September 8th, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Yevgeny Liokumovich (U of T)

Title: Minimal surfaces, metric geometry and scalar curvature

Abstract: Which manifolds admit metrics of positive scalar curvature? What are the geometric properties of such metrics? Minimal surfaces play a key role in the recent progress made in answering these questions. These developments also inspired new results about a macroscopic analog of scalar curvature in the geometry of metric spaces. I will describe the interplay between scalar curvature and macroscopic scalar curvature, and explain how this relationship yields new findings in both areas.

2023 Lorne Campbell Lecture Series

Friday, November 24th, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 127

Speaker: Prof. Gabor Lugosi (Univ. Pompeu Fabra, Spain)

Title: Mathematical Models of Network Archaeology

Abstract: Large networks that change dynamically over time are ubiquitous in various areas such as social networks, and epidemiology. These networks are often modeled by random dynamics which, despite being relatively simple, give a quite accurate macroscopic description of real networks. In \network archaeology" one studies statistical problems of inferring the past properties of such growing networks, given the current state of the network. In this talk, we discuss some simple network models and review recent results on revealing the past of the networks.

Bio: Professor Gabor Lugosi received the PhD degree in electrical engineering from the Hungarian Academy of Sciences. He is an ICREA (Catalan Institution for Research and Advanced Studies) Research Professor at the Department of Economics, Pompeu Fabra University, Barcelona, Spain. His main research interests include statistical learning theory, sequential prediction, nonparametric classication and regression, random graphs, and concentration inequalities.

Professor Lugosi has published over 120 papers and four research monographs, including Prediction, Learning, and Games in 2006 and Concentration Inequalities: A Nonasymptotic Theory of Independence in 2013. He has served on the editorial board of several journals including the Annals of Applied Probability, the Journal of Machine Learning Research and the IEEE Transactions on Information Theory. He has been \Medallion Lecturer" (2009) and \Blackwell Lecturer" (2021) of the Institute of Mathematical Statistics. He was an invited speaker at the 2022 International Congress of Mathematicians, and he delivered the \Breiman Lecture" in 2021 at NeurIPS, the prime conference on Machine Learning.

Number Theory Seminar

Wednesday, August 9th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 222

Speaker: Dominic Austria (Queen's University)

Title: Evaluating sums of arithmetic functions

Abstract: In the course of an ongoing research project I came across the curious sum: $\sum_{n\leq x} \frac{\lambda(n)}{\phi(d)}$ where $\lambda(n)$ is the Liouville lambda function and $\phi(n)$ is the usual Euler Totient function. I will discuss some of the various techniques used to study sums of such arithmetic functions using this example as the guiding tool.