The Algebraic Combinatorics Workgroup

Scheduled for Fridays at 3:30 PM (EDT [GTM -4]),
ONLINE Zoom meeting

A working seminar (at) of the Fields Institute organized by
Nantel Bergeron
and Aram Dermenjian.

Date Speaker Title (click titles for abstract) Sept 25 Nantel Bergeron, Aram Dermenjian, and Mike Zabrocki (all York) First meeting This is Zoom organization meeting, please come and present problem you would like to work on this year Oct 2 Mike Zabrocki SuperInvariants quotient and Harmonics Mike Zabrocki will go over our main conjecture from the beginning and go over the linear basis option.Oct 9 Nantel Bergeron Finding basis in quotient space Nantel Bergeron will go over the Artin basis in the classical case and the characterization he mentioned last week. And see what goes wrong for super harmonics. The Notes from the talk are HEREOct 16 Nantel Bergeron Toward constructing a basis for the Super-coinvariants We start showing our main long standing conjecture. I will present what I believe will lead us to a full proof. This is a draft attempt but it is promissing.Oct 23 Nantel Bergeron, Aram Dermenjian Toward constructing a basis for the Super-coinvariants part 2 We continue looking at a draft proof as presented by Nantel Bergeron.Oct 30 Aram Dermenjian Toward constructing a basis for the Super-coinvariants for n=5 We look at potential issues when n=5.Nov 06 Kelvin Chan Turning hooks into alternants We look at a construction that turns a hook shaped Specht module into an alternating polynomial.Nov 13 Kelvin Chan Turning hooks into alternants: part 2 We will continue from last week and look at a construction that turns a hook shaped Specht module into an alternating polynomial.Nov 20 Yohana Solomon Multiset Partition Algebra In this talk, we will introduce multiset partition algebra, whose basis elements are indexed by multiset partition.Nov 27 Aram Dermenjian An open problem on left regular bands, part 1 In this talk we discuss an open problem on left refular bands.Dec 4 Aram Dermenjian An open problem on left regular bands, part 2 In this talk we discuss an open problem on left refular bands.Dec 11 Aram Dermenjian An open problem on left regular bands, part 3 In this talk we discuss an open problem on left refular bands.Dec 18 Mike Zabrocki, Nantel Bergeron, Aram Dermenjian A recap of the semester In this talk we give an overview of the topics discussed this semester.

Date Speaker Title (click titles for abstract) Jan 22 Nantel Bergeron, Mike Zabrocki First meeting This is Zoom organization meeting, please come and present problem you would like to work on this year Jan 29 Nantel Bergeron Open problems on the 0/1-polytope In this talk we discuss open problems on 0/1-polytopes.Feb 5 Aram Dermenjian Left Regular Bands We will review left regular bands, giving new examples, and looking at conjectures we have made. In addition, we will present some counterexamples to some previously conjectured ideas.Feb 12 Mike Zabrocki Super Space Feb 19 Nantel Bergeron 0/1 Polytopes. Feb 26 Aram Dermenjian Left Regular Bands Mar 5 Mike Zabrocki Super Coinvariants I’ll define k-obstructed super-monomials as monomials m = X_n^a*T_n^b such that

* a_k + b_1 + … + b_k = k

* a_i + b_1 + … + b_i < i for 1 <= i < k

* a_j = b_j = 0 for j>k

I’ll show how to iterate through this set and enumerate the k-obstructed monomials. Then we will try to use this iterative structure to define elements g_m such that LT(g_m) = m.Mar 12 Nantel Bergeron Studying 0/1-polytopes arising from simplicial complexes. Mar 19 Aram Dermenjian Meet-semilattice left regular bands and a diversion We will present a theorem on when the face poset of a left regular band is a meet-semilattice and why this theorem is not satisfactory. If time allows we will talk about a certain diversion.

- Unless otherwise indicated, the seminar meets on Fridays at 3:30 pm ONLINE Zoom meeting . 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.