SCIENTIFIC PROGRAMS AND ACTIVITIES

October 25, 2014

Algebraic Combinatorics Seminar 2006-07
held at the Fields Institute

The purpose of this seminar is to cover exposition on topics of algebraic combinatorics which are of interest to the people attending, so please feel free to come and participate. For more informations, contact Christophe Hohlweg - chohlweg (at) fields.utoronto.ca

We also organize special sessions jointly with the Applied Algebra Seminar (York University)

Fields Working Sessions Tuesdays 12:00 p.m. - 1:30 p.m., unless otherwise indicated.

3-Apr-2007
12:00 p.m.
Franco Saliola, UQAM
Finding the Quiver of the Descent Algebras
This will be a survey outlining the current status of my project to study of the representation theory of the descent algebra of a finite Coxeter group. It will concentrate on the descent algebra of the symmetric group because the current results are better in this case. The approach utilizes what I call the "geometric approach" to the descent algebra: there is a semigroup algebra constructed from the reflection arrangement of the Coxeter group that contains the descent algebra. The quiver of this semigroup algebra will be constructed and it will be used to get information about the quiver of the descent algebra.
27-Mar-2007
12:00 p.m.
Nantel Bergeron, York University
Working Session: Finding knuth relations for a type B Robinson Schensted corespondence invoving Domino tableaux
27-Feb-2007
12:00 p.m.
Nantel Bergeron, York University
Generalization of the weak order on tableaux to Coxeter groups and related problems II
20-Feb-2007
12:00 p.m.
Nantel Bergeron, York University
Working Session: Generalization of the weak order on tableaux to Coxeter groups and related problems
13-Feb-2007
12:00 p.m.
Special Session
Srecko Brlek, UQAM
Variations on Cantor's celebrated diagonal argument
Given a square $n \times n$ tableau $T=\left(a_i^j\right)$ on a finite alphabet $A$, let $L $ be the set of its row-words. The permanent $\Perm(T)$ is the set of words $a_{\pi(1)}^1a_{\pi(2)}^2\cdots a_{\pi(n)}^n$, where $\pi$ runs through the set of permutations of $n$ elements. Cantorian tableaux are those for which $\Perm(T)\cap L=\emptyset.$ Let $s=s(n)$ be the cardinality of $A$. We show in particular that for large $n$, if $s(n) <(1-\epsilon) n/\log n$ then most of the tableaux are non-Cantorian, whereas if $s(n) >(1+\epsilon) n/\log n$ then most of the tableaux are Cantorian. We conclude our article by the study of infinite tableaux. Consider for example the infinite tableaux whose rows are the binary expansions of the real algebraic numbers in the unit interval. We show that the permanent of this tableau contains exactly the set of binary expansions of all the transcendental numbers in the unit interval.
12-Feb-2007
12:00 p.m.
Special Session
Amy Glen
, CRM-ISM-LaCIM, UQAM
Characterizations of finite and infinite episturmian words via lexicographic orderings
In this talk, I will present some new results arising from collaborative work with Jacques Justin (France) and Giuseppe Pirillo (Italy). This work, which extends previous results on extremal properties of infinite Sturmian and episturmian words, is purely combinatorial in nature. Specifically, we characterize by lexicographic order all finite Sturmian and episturmian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a wide sense (episturmian and episkew infinite words). That is, we characterize the set of all infinite words whose factors are (finite) episturmian. Similarly, we characterize by lexicographic order all balanced infinite words over a 2-letter alphabet; in other words, all Sturmian and skew infinite words, the factors of which are (finite) Sturmian.
06-Feb-2007
12:00 p.m.
Muge Taskin, York University and Fields
Problems on the weak order on tableaux, proofs II
30-Jan-2007
12:00 p.m.
Muge Taskin, York University and Fields
Problems on the weak order on tableaux, proofs I
23-Jan-2007
12:00 p.m.
Hugh Thomas, U. New Brunswick
Schiffler's formula for A_n cluster variables and some generalizations
We will present Schiffler's formula for expanding a cluster variable as a sum of Laurent monomials in the seed variables in the A_n case (as presented in math.RT/0611956). We will discuss a generalization in the context of Fomin-Shapiro-Thurston cluster algebras associated to surfaces, and a related result in which, for an acyclic seed, we give a formula to expand a cluster variables as a sum of standard monomials in the lower cluster algebra. The new results we will be discussing are joint with Ralf Schiffler.
16-Jan-2007
12:00 p.m.
Mike Zabrocki
Decomposition of a Gl_n irrep into S_n irreps, Part 3
12-Dec-2006
12:00 p.m.
Alejandra Premat
Part II of Crystal Bases
05-Dec-2006
12:00 p.m.
Mike Zabrocki
Decomposition of a Gl_n irrep into S_n irreps (data for n=6) (some conjectures and results)
28-Nov-2006
12:00 p.m.
Muge Taskin, York University and Fields
Solution to open problems
21-Nov-2006
12:00 p.m.
Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux part 3
14-Nov-2006
12:00 p.m.
Mike Zabrocki
An explanation of a problem of computing the restriction of a Gl_n module to S_n.
Remark: it is true that F_{S_n}( f g ) = F_{S_n}(f) * F_{S_n}(g) (example)

07-Nov-2006
12:00 p.m.
Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, isometry problem: proof Part 2
31-Oct-2006
12:00 p.m.
Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, isometry problem: proof Part 1
24-Oct-2006
12:00 p.m.
Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux Part 2
17-Oct-2006
12:00 p.m.
Muge Taskin, York University and Fields
Open problems related to some orders on standard Young tableaux Part 1
10-Oct-2006
12:00 p.m.
Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, open problems Part 2
03-Oct-2006
11:00 a.m.
Special Session
Christian Kassel, CNRS-Université Louis Pasteur, Strasbourg
A Hall algebra based on the projective line
(Joint work with Pierre Baumann)
One can construct a Hall algebra out of the vector bundles over a projective curve on a finite field. I'll describe this algebra in the case when the curve is a projective line. This algebra is related to the quantum affine algebra associated to the Lie algebra sl(2). In my talk I'll insist on the combinatorial aspects of the subject.

26-Sep-2006
12:00 p.m.
Alejandra Premat, York University and Fields
Introduction to Crystal basis
19-Sep-2006
12:00 p.m.
Christophe Hohlweg, Fields Institute
Permutahedra and Generalized Associahedra, open problems