The Algebraic Combinatorics Workgroup

Scheduled for Fridays at 3:15 PM (EDT [GTM -4]),

#### Schedule FALL 2022
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#### Schedule WINTER 2023
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A working seminar (at) of the Fields Institute organized by
Nantel Bergeron
and Kelvin Chan.

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 TBDDec 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.

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

- This is in collaboration with the Fields Institute.
- If you are interested in speaking at the seminar, contact Nantel Bergeron.
- You may also be interested in the Applied Algebra Seminar (Monday afternoons at York University).

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