The Algebraic Combinatorics Seminar

Schedule FALL 2017 Click to see schedule

Date Speaker Title (click titles for abstract)

Sept 15 Nantel Bergeron Organization, two problems:
1- symmetric functions in super space
2- The space of planar trees graded by signature.

Sept 22 Nantel Bergeron and Rafael S. González D'león The space of trees graded by signature.

Sept 29 Nantel Bergeron and Rafael S. González D'león The space of trees graded by signature.

Oct 6 Mike Zabrocki Symmetric functions in super space
I organized the big picture related to the goal of this project: there are a number of polynomial and non-commutative polynomial rings for which the invariants and quasi-invariants are well known Hopf algebras (Sym, QSym, NCSym, etc.). I described the minimal information that we need in order to implement Sym and QSym and left the symmetric functions in super space and the quasi-symmetric functions in super-space as the next steps.

Oct 13
At YORK Jerzy Wejman This will be a coloquium talk at YORK University. This week only

Oct 20 Mike Zabrocki Symmetric functions in super space
The following papers will be our main focus:

Classical symmetric functions in superspace

Pieri rules for Schur functions in superspace

Jack superpolynomials, superpartition ordering and determinantal formulas

Jack superpolynomials: physical and combinatorial definitions

Orthogonality of Jack polynomials in superspace

Macdonald polynomials in superspace as eigenfunctions of commuting operators

N>=2 symmetric superpolynomials

Also my code is can be accessed by executing the command:
load("http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py") and the code for superpartitions is at: http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py and http://garsia.math.yorku.ca/~zabrocki/superpartitions.py

Oct 27 Reading week

Nov 3 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees and stirling permutations (open questions in abstract)
Last time we define Hopf algebra on Planar Binary Trees using a process describe by Aguiar and Sotille using "lightening". This is isomorphic to Loday-Ronco Hopf algebra. We can label the binary trees incrisingly and the "lightening" process still work to define a Hopf algebra. This time it is the larger and correspond to permutations. It is the Malvenuto-Reutenauer Hopf algebra. It is nice to express everything in term of trees as it makes the operation more transparent and explain better the relation between those algebras. Now we can generalize as well very easily. Consider non-degenerate planar trees (no internal node of degree 1). The process of lightening still work well and we can define two Hopf algebras on those trees We can also consider increasing labeling of such trees and now many natural questions arises: SEE QUESTIONS transcripted by James

Nov 10 Mike Zabrocki Symmetric functions in super space
Last time we conjectured a formula for the Monomial and Fundamental quasi-symmetric functions in super space. We will need to work to refine and clarify the notation for these formulae and conjecture their product and coproduct in analogy with the monomial and fundamental bases of QSym.

Code for SuperCompositions and QuasiSymmetricFunctionsinSuperSpace (Monomial basis only) in Sage:
load("http://garsia.math.yorku.ca/~zabrocki/supercompositions.py")
load("http://garsia.math.yorku.ca/~zabrocki/superpartitions.py")
load("http://garsia.math.yorku.ca/~zabrocki/qsf_superspace.py")
load("http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py")

Nov 17 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees, stirling permutations and parking functions.

Nov 24 James Huang and Laura Colmenarjo P partition and Schur function in Symmetric functions in super space

Dec 1 Marcelo Aguiar
[Cornell U.] Integral Hyperplane Arrangements

Dec 8 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees, stirling permutations and parking functions.

Date	Speaker	Title (click titles for abstract)
Sept 15	Nantel Bergeron	Organization, two problems: 1- symmetric functions in super space 2- The space of planar trees graded by signature.
Sept 22	Nantel Bergeron and Rafael S. González D'león	The space of trees graded by signature.
Sept 29	Nantel Bergeron and Rafael S. González D'león	The space of trees graded by signature.
Oct 6	Mike Zabrocki	Symmetric functions in super space I organized the big picture related to the goal of this project: there are a number of polynomial and non-commutative polynomial rings for which the invariants and quasi-invariants are well known Hopf algebras (Sym, QSym, NCSym, etc.). I described the minimal information that we need in order to implement Sym and QSym and left the symmetric functions in super space and the quasi-symmetric functions in super-space as the next steps.
Oct 13 At YORK	Jerzy Wejman	This will be a coloquium talk at YORK University. This week only
Oct 20	Mike Zabrocki	Symmetric functions in super space The following papers will be our main focus: Classical symmetric functions in superspace Pieri rules for Schur functions in superspace Jack superpolynomials, superpartition ordering and determinantal formulas Jack superpolynomials: physical and combinatorial definitions Orthogonality of Jack polynomials in superspace Macdonald polynomials in superspace as eigenfunctions of commuting operators N>=2 symmetric superpolynomials Also my code is can be accessed by executing the command: `load("http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py")` and the code for superpartitions is at: `http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py` and `http://garsia.math.yorku.ca/~zabrocki/superpartitions.py`
Oct 27	Reading week
Nov 3	Rafael D'leon and Nantel Bergeron	Hopf algebra of planar trees and stirling permutations (open questions in abstract) Last time we define Hopf algebra on Planar Binary Trees using a process describe by Aguiar and Sotille using "lightening". This is isomorphic to Loday-Ronco Hopf algebra. We can label the binary trees incrisingly and the "lightening" process still work to define a Hopf algebra. This time it is the larger and correspond to permutations. It is the Malvenuto-Reutenauer Hopf algebra. It is nice to express everything in term of trees as it makes the operation more transparent and explain better the relation between those algebras. Now we can generalize as well very easily. Consider non-degenerate planar trees (no internal node of degree 1). The process of lightening still work well and we can define two Hopf algebras on those trees We can also consider increasing labeling of such trees and now many natural questions arises: SEE QUESTIONS transcripted by James
Nov 10	Mike Zabrocki	Symmetric functions in super space Last time we conjectured a formula for the Monomial and Fundamental quasi-symmetric functions in super space. We will need to work to refine and clarify the notation for these formulae and conjecture their product and coproduct in analogy with the monomial and fundamental bases of QSym. Code for SuperCompositions and QuasiSymmetricFunctionsinSuperSpace (Monomial basis only) in Sage: `load("http://garsia.math.yorku.ca/~zabrocki/supercompositions.py")` `load("http://garsia.math.yorku.ca/~zabrocki/superpartitions.py")` `load("http://garsia.math.yorku.ca/~zabrocki/qsf_superspace.py")` `load("http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py")`
Nov 17	Rafael D'leon and Nantel Bergeron	Hopf algebra of planar trees, stirling permutations and parking functions.
Nov 24	James Huang and Laura Colmenarjo	P partition and Schur function in Symmetric functions in super space
Dec 1	Marcelo Aguiar [Cornell U.]	Integral Hyperplane Arrangements
Dec 8	Rafael D'leon and Nantel Bergeron	Hopf algebra of planar trees, stirling permutations and parking functions.

Schedule WINTER 2018 Click to hide schedule

Date Speaker Title (click titles for abstract)

Jan 19 Laura Colmenarejo Quasisymmetric functions in superspace.
We review the work of Luc Lapointe and his colaborators on quasisymmetric functions in super space.

Jan 26 NO SEMINAR We attend CAAC conference in McMaster

Feb 2 Nantel Bergeron A new working topic (see link to documents bellow)
This winter we will continue to work on
(a) quasysymmetric functions in superspace
(b) Hopf algebra of trees (when Rafael is available)
(c) A new topic... We will find out on This day! I am now attaching document and more to come
Picture of a permutahedron.
This is a PDF that contains the question
This is a PDF that contains picture and some partial solution

Feb 9 Mike Zabrocki Harmonics in super space
We will look at the quotient of the polynomial ring in a commuting and anti-commuting set of variables mod the ideal generated by the symmetric functions in superspace.

Feb 16 Mike Zabrocki Harmonics in super space
We look at the Frobenius series of the harmonics in super space.

Feb 23 NO SEMINAR (reading week)

Mar 2 Nantel Bergeron Kernel of $\Theta\circ\Psi\circ\Psi^*\circ\Theta^*$.
We define the Hopf monoid involved and some of the maps.

Mar 9 Mike Zabrocki Harmonics in super space.
Continuing with the super-harmonic space we will talk about conjectures and techniques for finding formulas for the Hilbert series and Frobenius series. (data)

Mar 16 Rafael Gonzales D'leon and Nantel Bergeron Continuing project of Hopf algebra of planar trees we start at 3:10... trying to connect with Rafael

Year	Topic
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

Date	Speaker	Title (click titles for abstract)
Jan 19	Laura Colmenarejo	Quasisymmetric functions in superspace. We review the work of Luc Lapointe and his colaborators on quasisymmetric functions in super space.
Jan 26	NO SEMINAR	We attend CAAC conference in McMaster
Feb 2	Nantel Bergeron	A new working topic (see link to documents bellow) This winter we will continue to work on (a) quasysymmetric functions in superspace (b) Hopf algebra of trees (when Rafael is available) (c) A new topic... We will find out on This day! I am now attaching document and more to come Picture of a permutahedron. This is a PDF that contains the question This is a PDF that contains picture and some partial solution
Feb 9	Mike Zabrocki	Harmonics in super space We will look at the quotient of the polynomial ring in a commuting and anti-commuting set of variables mod the ideal generated by the symmetric functions in superspace.
Feb 16	Mike Zabrocki	Harmonics in super space We look at the Frobenius series of the harmonics in super space.
Feb 23		NO SEMINAR (reading week)
Mar 2	Nantel Bergeron	Kernel of $\Theta\circ\Psi\circ\Psi^\circ\Theta^$. We define the Hopf monoid involved and some of the maps.
Mar 9	Mike Zabrocki	Harmonics in super space. Continuing with the super-harmonic space we will talk about conjectures and techniques for finding formulas for the Hilbert series and Frobenius series. (data)
Mar 16	Rafael Gonzales D'leon and Nantel Bergeron	Continuing project of Hopf algebra of planar trees we start at 3:10... trying to connect with Rafael