The Applied Algebra Seminar
A Monday afternoon research seminar

About the seminar (click here to see more)

The seminar is currently organized by Lucas Gagnon and Nantel Bergeron.


Dates are listed in reverse-chronological order. Unless otherwise indicated, all in person talks will take place on Monday from 15:00-16:00 in N638 Ross Building (York University).

Spring 2024

Date Speaker Title (click titles for abstract)
15 April 2024
Kartik Singh
U. Waterloo
8 April 2024
Blessing Oni
(Fields Inst.)
1 April 2024 Karen Yeats
(U. Waterloo)
25 March 2024
Sooyeong Kim
(York U.)
18 March 2024 Eric Sommers
(UMass Amherst)
11 March 2024
Travis Scrimshaw
(Hokkaido University)
4 March 2024 Vasu Tewari
(U. Toronto)
26 Feb. 2024
Timothy Miller
(U. Waterloo)
Vertex models for the product of a Schur and Demazure polynomial
Demazure atoms and characters are polynomials that each form a Z-basis for polynomials in n variables. The product of a Schur polynomial with a Demazure atom (resp. character) expands into a linear combination of Demazure atoms (resp. characters) with positive integer structure coefficients. There are known combinatorial rules that compute these coefficients using "skyline tableaux" given by Haglund, Luoto, Mason and Willigenburg. I have found alternative rules using the theory of integrable vertex models, inspired by a technique introduced by Zinn-Justin. I use "coloured" vertex models for atoms and characters obtained from Borodin and Wheeler's models for non-symmetric Macdonald polynomials (setting q=t=0). The structure coefficients are then obtained as the number of fillings of a "diamond" vertex model that is compatible with both Schur (uncoloured) and Demazure (coloured) vertex models. The proof is completely combinatorial and very pretty.
19 Feb. 2024 Reading Week
12 Feb. 2024
No Monday seminar See talk in Algebraic Combinatorics working seminar
5 Feb. 2024 George Seelinger
(U. Michigan)
Raising operator formulas for Macdonald polynomials and other related families
Macdonald polynomials are a basis of symmetric functions with coefficients in $\mathbb{Q}(q,t)$ exhibiting deep connections to representation theory and algebraic geometry. In particular, specific specializations of the $q,t$ parameters recover various widely studied bases of symmetric functions, such as Hall-Littlewood polynomials, Jack polynomials, q-Whittaker functions, and Schur functions. Central to this study is the fact that the Schur function basis expansion of the Macdonald polynomials have coefficients which are polynomials in $q,t$ with nonnegative integer coefficients, which can be realized via a representation-theoretic model. Surrounding this line of inquiry, a rich theory of combinatorics emerged, encoded in symmetric functions with expansions of the Macdonald polynomials into LLT polynomials via the work of Haglund-Haiman-Loehr, among others. LLT polynomials were first introduced by Lascoux-Leclerc-Thibbon as a q-deformation of a product of Schur polynomials and have appeared in various related contexts since their introduction. In this talk, I will explain this background and provide a new explicit "raising operator" formula for Macdonald polynomials, proved via an LLT expansion, with a detour showing how similar raising operator formulas can provide a bridge between algebraic and combinatorial formulations of some other symmetric functions. This work is joint with Jonah Blasiak, Mark Haiman, Jennifer Morse, and Anna Pun.

Fall 2023


Below you will find links to the seminar webpages for previous years.
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Year 2011-12 Year 2010-11 Year 2009-10 Year 2008-09 Fall 2007
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