The Algebraic Combinatorics Seminar

Scheduled for Fridays at 3:00 PM

In reverse-chronological order.

Date Speaker Title (click titles for abstract) 15 Apr. 2016

Nantel Bergeron Toward a cancelation free formula for the antipode of Hypergraphs (Part IV: Orientations) 8 Apr. 2016

Nantel Bergeron Toward a cancelation free formula for the antipode of Hypergraphs (Part III: Hopf Monoid structure) 1 Apr. 2016

Iain Moffat (University of London) The Tutte Polynomial via Hopf algebras The Tutte polynomial is one of the most important, and best studied, graph polynomials. It is important not only because it encodes a large amount of combinatorial information about a graph, but also because of its applications to areas such as statistical physics and knot theory. Because of its importance the Tutte polynomial has been extended to various classes of combinatorial object. For some objects there is more than one definition of a "Tutte polynomial". For example, there are three different definitions for the Tutte polynomial of graphs in surfaces: M. Las Vergnasâ€™ 1978 polynomial, B. BollobÃ¡s and O. Riordanâ€™s 2002 ribbon graph polynomial, and V. Kruskalâ€™s polynomial from 2011. On the other hand, for some objects, such as digraphs, there is no wholly satisfactory definition of a Tutte polynomial. Why is this? Why are there three different Tutte polynomials of graphs in surfaces? Which can claim to be the Tutte polynomial of a graph in a surface? More generally, what does it mean to be the Tutte polynomial of a class of combinatorial objects? In this talk I will describe how Hopf algebras can be used to canonically construct Tutte polynomials of combinatorial objects, and, using this framework, will offer answers to these questions. This is joint work with Thomas Krajewski and Adrian Tanasa.11 Mar. 2016

Mike Zabrocki Character evaluated at root of unity and Kronecker product of symmetric functions(Hopf Structure) 4 Mar. 2016

Shu Xiao Li The quotient k[x,y]/ , part II We continue work on the quotient k[x,y]/. This time, we focus on the case of infinitely many variables. I will attempt to construct explicitly its hilbert basis and give a proof. Hopefully we could also discuss about the case of finitely many variables. 26 Feb. 2016

Nantel Bergeron Toward a cancelation free formula for the antipode of Hypergraphs (Part II: and total order) 12 Feb. 2016

Nantel Bergeron Toward a cancelation free formula for the antipode of Hypergraphs (Part I: the Graph case) 5 Feb. 2016

Mike Zabrocki Character evaluated at root of unity and Kronecker product of symmetric functions( The h-tilde basis) 29 Jan. 2016

Mike Zabrocki Character evaluated at root of unity and Kronecker product of symmetric functions 22 Jan. 2016

SPECIAL TalkYuly Billig

(Carleton University)Sturm-Liouville problem in Fock space We compute the eigenvalues of the differential operator \Sum_{a+b=c+d} x_a x_b d/dx_c d/dx_d acting on the Fock space C[x_1, x_2, ...]. It turns out that this operator is diagonalizable with integer non-negative eigenvalues. Not surprisingly, the eigenvectors and the eigenvalues are indexed by Young diagrams.15 Jan. 2016

Shu Xiao Li We discuss the quotient of polynomials in two sets of variables by the diagonaly-quasysymmetric function and show some partial results 27 Nov. 2015

Sirous Homayouni Fomin-Kirillov algebra Buchberger's algorithm generates a Grobner basis ($GB$) for $I$, the ideal generated by the relations among generators $ x_{ij}=-x_{ji} $ of Fomin-Kirillov algebra $FK(n)$. We show that elements of any degree $d$, of a $GB$ (with a polynomial ordering) generated by Buchberger's algorithm for the ideal $I$, are \textit{z-star} polynomials, i.e., polynomials with all variables of the form $x_{\alpha z}$, for a fix $z$, where $1\leq\alpha20 Nov. 2015

Nantel Bergeron Quotient involving Combinatorial Hopf Algebra I will show that as we pass from n to n+1, The basis of the quotient for n is included in the quotient for n+1. In fact I show several potential inclusion that has consequences on the structure of the Hilbert series of the quotient. I will also recall that when we have free Hopf algebra we can determine the infinite Hilbert series. I will do so for quotient of r-QSym/s-QSym. That last part was inspired by talks during A. Lauve's visit.13 Nov. 2015

Shu Xiao Li discussion on the dimension of quotients involving r-quasisymmetric functions 6 Nov. 2015

Farid Aliniaeifard The dimension of the quotient of polynomials by ideal generated by non-constant generalized quasi-symmetric functions We consider a certain action of the symmetric group on polynomials called local action. Then we try to find the dimension of the quotient of polynomials by the ideal generated by the orbits of the local action.30 Oct. 2015

Mike Zabrocki Symmetric group and Gl_n characters I will review the construction of the Gl_n and S_n characters in the tensor algebra and then present a simple to state open problem: how do we express the S_n characters as a monomial symmetric function expansion in the eigenvalues of the permutation matrix?23 Oct. 2015

Room 230Shu Xiao Li Unimodality and Fibonomials 16 Oct. 2015

Nantel Bergeron Hopf monoid of Matroid and Positroid I describe the Hopf monoid of matroid (with linear order) and the Hopf submonoid of Positroid.9 Oct. 2015

Room 230Yannic Vargas The product of monomial basis in the Hopf algebra of Malvenuto-Reutenauer We will work out some examples to understand two combinatorial interpretations for the coefficients of the product between the monomial basis in the Hopf algebra of Malvenuto-Reutenauer, based on planar posets and permutation patterns.2 Oct. 2015

NO SEMINAR25 Sep. 2015 Nantel Bergeron and Carolina Benedetti Hopf algebras on matroids We will work out some examples of the several Hopf algebras on Matroids.18 Sep. 2015 Jean-Baptiste Priez Non-commutative Frobenius characteristic of generalized parking functions 11 Sep. 2015 Nantel Bergeron What to do this year 27 Aug. 2015 Tom Denton (Google Inc) How to Win a Data Science Competition With Algebraic Combinatorics As an early foray into the intersection of combinatorics and machine learning, I tried my hand at a Kaggle competition on identifying circles of friends in the Facebook graph. I'll give an overview of my solution, including a deep dive on spectral clustering, a graph clustering algorithm with roots in algebraic graph theory.21 Aug. 2015

SERIES of TALKSCarolina Benedetti Matroid, Positroid and Combinatorial Hopf Algebras. 14 Aug. 2015

SERIES of TALKSCarolina Benedetti Matroid, Positroid and Combinatorial Hopf Algebras. 7 Aug. 2015

SERIES of TALKSCarolina Benedetti Matroid, Positroid and Combinatorial Hopf Algebras.

- Unless otherwise indicated, the seminar meets on Fridays at 3:15 pm in Room 210 of 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.