ºÚÁϳԹÏ×ÊÔ´

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.

Advances in Representation Theory of Algebras IX (ARTA)

June 12th-16th, 2023

Dynamics, Geometry and Groups Seminar

Wednesday, May 10th, 2023

Time: 3:30 p.m.  Place: Jeffery Hall, Room 422

Speaker: Rémi Coulon (Université de Rennes)

Title: Growth problems in negatively curved groups

Abstract: Given a group G acting by isometries on a metric space X, its exponential growth rate provides a way to measure the "size" of its orbits. More precisely it quantifies te asymptotic behavior of the number of orbit points in a ball. When G is the fundamental group of a compact hyperbolic manifold M acting on the universal cover X of M, then this rate has numerous interpretations both of geometric and dynamical nature. In particular it is the entropy of the geodesic flow on the unit tangent bundle of M. In this configuration the study of the geodesic flow on M (and its covers) provides useful informations on the growth rates of G and its subgroups.

In this talk we will present a work in progress whose aim is to exploit similar techniques, while strongly relaxing the hypothesis on the curvature of X. For our purpose, it suffices to assume that the group G contains a "contracting element', which can be thought of as a "hyperbolic direction". Besides fundamental groups of hyperbolic manifolds, this general framework encompasses (relatively) hyperbolic groups, modular groups of surfaces, many right angled Artin groups, etc. As an application we will provide an amenability criterion for the quotients of G.

Algebra & Geometry Seminar

Tuesday, April 17th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 222

Speaker: Lucas Gagnon (York University)

Title: Quasisymmetric varieties, excedance classes, and bases for the Temperley–Lieb algebra

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Math Club

Thursday, April 6th, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: David Wehlau (RMC & ºÚÁϳԹÏ×ÊÔ´)

Title: Proofs from the Book

Abstract: The Hungarian Mathematician Paul Erdös (1913-1996) was one of the top mathematicians of the past century. He published more mathematical articles during his lifetime than anyone else in history. He did this by being utterly consumed by mathematics to the exclusion of all else.

Erdös believed that every mathematical result had one best, most elegant proof and that such proofs were recorded in one volume, known to Erdös as ``The Book''. I will describe some of Erdös' life and explain a few proofs that may be in The Book. I will start with the question: If $a$ and $b$ are irrational can $a^b$ be rational? There is an answer to this question that I believe belongs in The Book.

Probability Seminar

Wednesday, April 5th, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Alex Dunlap (NYU)

Title: The nonlinear stochastic heat equation in the critical dimension

Abstract: I will discuss a two-dimensional stochastic heat equation with a nonlinear noise strength, and consider a limit in which the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor. The limiting pointwise statistics can be related to a stochastic differential equation in which the diffusivity solves a PDE somewhat reminiscent of the porous medium equation. This relationship is established through the theory of forward-backward SDEs. I will also explain several cases in which the PDE can be solved explicitly, some of which correspond to known probabilistic models. This talk will be based on current joint work with Cole Graham and earlier joint work with Yu Gu.