ºÚÁϳԹÏ×ÊÔ´

Math & Stats Department Colloquium

Friday, October 8th, 2021

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

Speaker: Julian Sahasrabudhe (University of Cambridge)

Title: Probabilistic combinatorics at exponentially small scales

Abstract: In this talk I will discuss a set of tools that has recently been developed to think about events of extremely small probability in finite probability spaces. I try to will weave together how this sort of thinking was used to solve two longstanding problems in two different fields: an old problem of Littlewood in harmonic analysis, and an exponential bound on the singularity probability of a random symmetric matrix.

Julian Sahasrabudhe is a university lecturer (assistant professor in the Canadian system) in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He was a Junior Research Fellow at Peterhouse, University of Cambridge from 2017 to 2021. He got his Ph.D. in Mathematics at the University of Memphis in 2017. He is interested in extremal and probabilistic combinatorics, and intersections with probability, analysis and combinatorial number theory. Most recently, he has been interested in random polynomials and random matrices. He was awarded the European Prize in Combinatorics in 2021.

Algebra & Geometry Seminar

Monday, September 27th, 2021

Time: 4:30 p.m.  Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)

Speaker: Charles Paquette (Royal Military College & Queen's University)

Title: Simple representations over free products of semi-simple algebras via quivers.

Abstract: This is a report on joint work with Andrew Buchanan, Ivan Dimitrov, Olivia Grace, David Wehlau and Tianyuan Xu. We consider a free product $A$ of semi-simple $\mathbb{K}$-algebras over an algebraically closed field and show how representation theory of a suitable finite acyclic quiver $Q$ can be used to understand the representation theory of $A$. In particular, we show that the simple $A$-modules correspond to stable representations of $Q$ for some stability parameter. We apply this to the representation theory of free products of finite groups.

Website details here:

Math & Stats Department Colloquium

Friday, October 1st, 2021

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

Speaker: David Sumpter (University of Uppsala)

Title: Are there Ten Equations that rule the world? And if so, what are they?

Abstract: I describe ten key equations you need to know in order to make better decisions, understand the filter created by social media and even to be a better person. Using examples, such as ‘deciding whether your new boss is an idiot?’, 'deciding when to stop watching a Netflix series' and ‘buying new headphones’, I present some new ways of seeing some of our favourite mathematical results. I also describe these equations' role in society: in finance, gambling, social media and artificial intelligence. Surprisingly few people in the general public understand these key equations and the small group that do are becoming increasingly rich and powerful. I think there are (order) ten equations that rule the world and we have to learn how to use them and spread their usage.

David Sumpter is Professor of Applied Mathematics at the University of Uppsala, Sweden. He is the author of Soccermatics and Outnumbered, which have been translated into ten languages, and Collective Animal Behaviour, the leading text in the academic field he helped create. He has worked with a number of the world's biggest football clubs, advising on analytics, as well as consulting on betting.

Video of David Sumpter's talk (mp4, 1.7 GB)

Algebra & Geometry Seminar

Monday, September 20th, 2021

Time: 4:30 p.m.  Place: Online via Zoom (contact Kaveh Mousavand for Zoom link)

Speaker: Kaveh Mousavand (Queen's University)

Title: Module varieties of biserial algebras.

Abstract: Biserial algebras form and important family of tame algebras which contain several interesting families, such as gentle, string and special biserial algebras. In our ongoing joint work with Charles Paquette, we have verified a recent conjecture on the behavior of Schur representations (a.k.a bricks) over biserial algebras. This allows us to better describe the behavior of irreducible components of moduli spaces of representations over biserial algebras and also relate our results to the recent work of Chindris-Kinser-Weyman on the semi-invariants of the ring of polynomials of every such components.

Website details here:

Math & Stats Department Colloquium

Friday, September 24th, 2021

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

Speaker: Eric Rowland (Hofstra University)

Title: Congruences for some sequences arising in combinatorics.

Abstract: Over the last 15 years there have been a number of papers studying congruence properties of sequences such as the Catalan numbers that arise in combinatorial settings. Proofs of these properties have relied on methods particular to each sequence. However, by realizing a sequence as the diagonal of a rational power series in multiple variables, we can compute congruence information modulo prime powers in a completely automatic way. This approach reduces the proofs of many known results to routine computations, establishes new theorems for well-known sequences, and allows us to resolve some conjectures about the Apery numbers.

Eric Rowland is an Associate Professor of Mathematics at Hofstra University. Before joining Hofstra, he held postdoctoral positions at Tulane University, the University of Waterloo, the University of Quebec at Montreal, and the University of Liege. He got his Ph.D. in Mathematics in 2009 from Rutgers University. He studies arithmetic properties of integer sequences that arise in combinatorial settings. His research involves a nice mix of number theory, combinatorics, and theoretical computer science.

Title: Measuring hypersurface singularities via differential operators and Hodge theory.

Abstract: Given a polynomial with complex coefficients, its set of zeros is a geometric object known as an algebraic hypersurface. We will discuss two invariants defined via differential operators that can detect and measure singularities of these hypersurfaces: the Bernstein-Sato polynomial and the Hodge ideals. Via the example of the hypersurface defined by the n x n determinant, we will illustrate that these invariants are two sides of the same coin: the mixed Hodge structure.

Michael Perlman is Coleman Postdoctoral Fellow in the Department of Mathematics and Statistics at Queen's University. He obtained his Ph.D. in Mathematics in May 2020 from the University of Notre Dame. His research is in Algebraic Geometry, Commutative Algebra, and their interactions with Representation Theory.