The Algebraic Combinatorics Workgroup
Scheduled for Fridays at 3:15 PM (EDT [GTM -4]),
A working seminar (at) of the Fields Institute organized by Nantel Bergeron and Kelvin Chan.


Schedule FALL 2022 Click to see/hide schedule

Date Speaker Title (click titles for abstract)
Sept 2 Lucas Gagnon (York), Anthony Aurthur Lazzeroni Jr (HKBU), Farhad Soltani (York), Nantel Bergeron (York) First Meeting. Icebreaker and Problem Suggestions
A few people will present some icebreaker talks and suggest some open problems.
Sept 9 Farhad Soltani (York) DQSYM
I will be talking about quasisymmetric polynomials on two sets of variables and the coinvariant space.
Sept 16 Lucas Gagnon (York) Chromatic quasisymmetric functions and representation theory
This talk will explore several topics related to the chromatic symmetric function and its quasisymmetric q-analogue. First, I will use them as a way to reviewt (quasi-)symmetric functions and some of their properties. Then, I will talk about some representation theoretic interpretations for symmetric functions generally, and the chromatic quasisymmetric function in particular.
Sept 23 Anthony Aurthur Lazzeroni Jr (HKBU) The ideal of r-quasisymmetric functions
In this talk I will recall the space of r-quasisymmetric functions. These spaces are nested subHopf algebras that interpolates between the space of Quasisymmetric functions and Symmetric functions. I will also discus some previous results about the quotient ring of the polynomial ring and the ideal generated by non-constant homogenous quasisymmetric functions.
Sept 30 Alan Lao (York) The matroid represented by adjacency matrix of a graph
The polygon matroids (or cycle matroids) of graphs have been extensively studied. I am going to introduce parts of the works by Brijder R., Hoogeboom H. J. and Traldi L. on the adjacency matroids of graphs. In particular we will look at the effect of "loop pivoting" on the adjacency matroids, and we will also see that "loop pivoting" can be seen as an action on a system which is another way of representing a graph.
Oct 7 Nantel Bergeron (York) Polytopes and Gröbner theory
We will review some background on polytopes and Gröbner theory. Then we will collectively explore using Gröbner theory to study properties of polytopes.
Oct 14 N/A Cancelled (reading week)
Oct 21 Kelvin Chan (York) Super harmonics
Super harmonics are anticommuting variants of diagonal harmonics introduced in this seminar series back in 2018. We will trace a little bit of its history and talk about some progress and open problems.
Oct 28 Nancy Wallace (York) Decomposing Diagonal Harmonics into GL_2\times S_n bicharacters
We will see what this means, point out some open problems related to this and talk about some progress. We will end by explaining the relation between diagonal harmonics and Shi arrangements.
Nov 4 Nantel Bergeron (York) QSym varities continued
We will continue our discussion on QSym varities from 3 weeks ago.
Nov 11 Anthony Aurthur Lazzeroni Jr (HKBU), Lucas Gagnon (York) Group effort!
We will have a group talk today. Various people will discuss progress of their projects.
Nov 18 Yohana Solomon (York) Hopf Algebra of Permutations
We will review the combinatorial description of the Malvenuto-Reutenauer Hopf algebra of permutations, and define a new basis for this algebra.
Nov 25 Nantel Bergeron (York) QSym varieties continued continued
TBD
Dec 2 N/A Cancelled due to conflict with CMS Winter meeting.
None.
Dec 9 Anthony Aurthur Lazzeroni Jr (HKBU) r-QSym coinvariants continued
See title. :)
Dec 16 Kelvin Chan (York) A potential leading term argument for super harmonics
We will examine some data that suggests there is a leading term argument for the conjectured basis of super harmonics.

Schedule WINTER 2023 Click to see/hide schedule

Date Speaker Title (click titles for abstract)
Jan 27 Curran McConnell (York) Weingarten Functions and Second-Order Finite Free Probability
Finite free probability is a field concerned with the eigenvalues of random matrices, especially under the operation of matrix addition. The matrix A+UBU* is of particular importance, where U is a Haar-distributed random unitary matrix, and A and B are deterministic matrices. The "first-order" behaviour of this random matrix's characteristic polynomial, i.e., its expected value, is well understood. I am working to develop the theory of its second-order behaviour, i.e., its covariance matrix. Narrowing in on the variance of the determinant of A+UBU*, I will describe how Weingarten functions connect Haar unitary matrices with the representation theory of the symmetric group.
Feb 3 (tentative) Nantel Bergeron (York)
Feb 10 (tentative) Kelvin Chan (York) Kernels of polarization operators
Feb 17 (tentative)
Feb 24 N/A Cancelled (reading week)
Mar 3
Mar 10
Mar 17
Mar 24
Mar 30
Apr 7 N/A Cancelled (Good Friday)
Mar 14

Notes.


About the seminar. Every year we pick a new topics to explore.

Year Topic
2020-2021 Super Harmonics, Left Regular Bands, and 0/1 Polytopes.
2019-2020 Super Harmonics and some sign variations.
2018-2019 Super Harmonics, steep bounce and a little bit of q-fibonomials.
2017-2018 (Quasi)symmetric functions in superspace, Hopf algebra of planar trees
2016-2017 Quantum Schubert; The theta map; Reduce order of symmetric group; Branching rule between GL(n) and symmetric group.
2015-2016 Positroid and Matroid/ Hopf algebras and quotients.
2014-2015 Fiboland, Symmetric and non symmetric functions
2013-2014 Fiboland, a world of Catalan and Fibonacci numbers
2012-2013 NSym and the Immaculate Basis
2011-2012 k-Schur functions and affine permutations
2010-2011 Littlewood Richardson rule k-Schur functions.
2009-2010 Idempotents and weakly ordered semigroups. (q,t) Catalan Numbers.
2008-2009 Littlewood-Richardson Rule, Shifted Tableaux and P-Schur functions
2007-2008 Open problems around k-Schur functions and non-commutative symmetric functions
2006-2007 Open problems
2005-2006 Cluster Algebras and Quivers
Spring 05 Formal languages and analytic classes of functions
Fall 04 (Quasi-) Symmetric functions in noncommutative variables and applications
Winter 03 Crystal Bases and Representation Theory, Super-algebras, etc.
Fall 03 Quasi-Symmetric functions and applications
Fall 02 Crystal Bases and Representation Theory