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 HarmonicsMike 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 spaceNantel 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 HERE Oct 16 Nantel Bergeron Toward constructing a basis for the Super-coinvariantsWe 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 2We 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=5We look at potential issues when n=5. Nov 06 Kelvin Chan Turning hooks into alternantsWe look at a construction that turns a hook shaped Specht module into an alternating polynomial. Nov 13 Kelvin Chan Turning hooks into alternants: part 2We 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 AlgebraIn 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 1In this talk we discuss an open problem on left refular bands. Dec 4 Aram Dermenjian An open problem on left regular bands, part 2In this talk we discuss an open problem on left refular bands. Dec 11 Aram Dermenjian An open problem on left regular bands, part 3In this talk we discuss an open problem on left refular bands. Dec 18 Mike Zabrocki, Nantel Bergeron, Aram Dermenjian A recap of the semesterIn this talk we give an overview of the topics discussed this semester.
Schedule WINTER 2021 Click to see/hide schedule
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-polytopeIn this talk we discuss open problems on 0/1-polytopes. Feb 5 Aram Dermenjian Left Regular BandsWe 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 CoinvariantsI’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 diversionWe 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.
Year Topic 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