This is the website for the Algebraic and Enumerative Combinatorics Seminar at the University of Waterloo. We view algebraic combinatorics broadly, explictly including algebraic enumeration and related asymptotic and bijective combinatorics as well as algebraic combinatorics as it appears in pure algebra and in applications outside mathematics.
We begin with a pre-seminar which is designed to get participants up to speed on useful and interesting background for the talk. It will be at the level for beginning grad students. Then there will be a short coffee break followed by the seminar itself.
Our audience consists principally of combinatorics faculty and grad students. Seminar talks are 50 minutes with questions following.
If you are speaking, we need your abstract at least a week in advance so it can make the deadline for the Friday math faculty seminar mailing.
Spring 2026
Usual location and time: 1:30 pre-seminar, 2:30 seminar, both in MC 5479.
Tuesday, May 5 in MC 6029: Siddhartha Sahi, Hypergeometric functions of matrix argument Click here for abstract
In a widely circulated manuscript from the 1990s, I.G. Macdonald introduced certain higher-rank analogs of the classical hypergeometric functions $_pF_q$, which are expressed as explicit series in Jack and Macdonald polynomials in one and two sets of variables. For special choices of parameters, these series reduce to the hypergeometric functions of matrix argument introduced earlier by C. Herz and A.T. James, which have numerous applications in number theory, multivariate statistics, signal processing, and random matrix theory.
The classical hypergeometric functions are solutions to the hypergeometric differential equation. Macdonald raised the problem of providing an analogous characterization for higher-rank functions by means of differential equations. Over the years, this problem was solved for a small number of cases where p and q are at most 3. However, as the operators become increasingly complicated, the general problem remained open for 40 years. In this talk, we will present a complete solution. This is joint work with Hong Chen.
May 21: Kaveh Mousavand, Left modularity and extremality of some (finite and infinite) lattices via representation theory Click here for abstract
Motivated by the representation theory of finite-dimensional algebras, we recently investigated the notions of left modularity and extremality in (completely) semidistributive lattices. For lattices of torsion classes, we obtain a simultaneous characterization of left modularity and extremality in terms of the behavior of certain indecomposable modules, called bricks. Our results extend the classical theory beyond the realm of finite lattices, while remaining within the framework of (completely) semidistributive lattices. Time permitting, I will also discuss extensions of these results to arbitrary infinite lattices that are completely semidistributive and weakly atomic. This talk is based on recent joint work with Sota Asai, Osamu Iyama, and Charles Paquette.
During the pre-seminar, after reviewing some basic notions from the representation theory of finite-dimensional algebras through the language of quiver representations, I will recall the classical notion of directedness and compare it with our new generalization, called brick-directedness. I will then discuss some basic properties of torsion classes and compare the notions of splitting and brick-splitting torsion pairs. No prior background in the representation theory of algebras will be assumed.
May 28: Sergio Alejandro Fernandez de Soto Guerrero
June 4 in MC 6460: Theodore Morrison
June 8 (Monday) and 9 (Tuesday) in TBD: Watch party for AlCoVE 2026, from 10am to 6pm.
June 11 in MC 6460: Kevin Purbhoo
June 18 in MC 6460: Scott Neville
June 25 in MC 6460: Mike Cummings
July 2: Jerónimo Valencia-Porras, Type C multiline queues and the open-boundary TASEP