6 June 4 p.m.
(Special Session) |
Anouk Bergeron-Brlek
TBA
|
18 April 4 p.m.
(Special Session) |
Muge
Taskin (Fields)
Plactic relations for r-domino tableaux
The recent work of Bonnafé et al. (2007) shows through
two conjectures that r-domino tableaux have an important role
in Kazhdan-Lusztig theory of type B with unequal parameters.
In this paper we provide plactic relations on signed permutations
which determine whether given two signed permutations have the
same insertion r-domino tableaux in Grafinkle’s algorithm
(1990). Moreover, we show that a particular extension of these
relations can describe Garfinkle’s equivalence relation
on r-domino tableaux
which is given through the notion of open cycles. With these
results we articulate the conjectures of Bonnafé, Geck,
Iancu, and Lam by providing necessary tools for their proof.
|
11 Apr. 4 p.m.
(Special Session) |
Muriel
Livernet (MIT)
Posets, Groups and Hopf algebras associated to a set-operad.
In this talk we will review a result of Bruno Vallette linking
the notion of Koszul duality for operads and Cohen-MacCauley
posets. We'll present in this context a joint work with F. Chapoton,
where we compare two Hopf algebras, one built directly from
operads, and another one associated to the incidence Hopf algebra
of a family of posets. This leads us to a new link between the
Hopf algebra ofConnes and Kreimer in renormalisation theory
and operads built on rooted trees. |
| 22 Feb. 4 p.m. |
John
Irvine (Saint Mary's University, Halifax)
Counting Lattice Paths Under a Shifting Boundary
The generalized ballot theorem gives a well-known formula for
the number of lattice paths in the first quadrant lying weakly
under the line x=ay, where a is an arbitrary positive integer.
While there is no simple formula for the number of paths under
an arbitrary piecewise linear boundary, we show that nice enumerative
results are available if we allow for cyclic shifts of such
a general boundaries. We show how our formula quickly yields
recent results concerning paths dominated by periodic boundaries.
A refinement allows for the counting of paths with a specified
number of corners. This is joint work with A. Rattan. |
| 15 Feb. 4 p.m. |
TBA |
| 8 Feb. 4 p.m. |
Nantel
Bergeron
New developements on the filtration of diagonal harmonics
|
| 1 Feb. 4 p.m. |
Mahir
Can (University of Western Ontario)
Some plethystic identities regarding the diagonal harmonics
module.
The Garsia-Haglund proof of the (q,t)-Catalan conjecture makes
use of plethystically defined, still mysterious, symmetric functions
$E_{n,k}$. In this talk, we present several symmetric function
identities involving the functions $E_{n,k}$.
If the time permits, We will also talk (speculate) about a seemingly
forgotten conjecture of Garsia and Haglund on the sectionalization
of the diagonal harmonics module.
-No prior background on the subject is expected.-
|
| 25 Jan. 4 p.m. |
Working
session focused on new developments about generalizations of
q,t-Catalan numbers
|
| 11 Jan. 4p.m. |
Nick
Loehr (Virginia Tech)
Combinatorial Aspects of the Bergeron-Garsia Nabla Operator
The nabla operator introduced by Francois Bergeron and Adriano
Garsia plays a key role in the theory of symmetric functions
and Macdonald polynomials. Over the past decade, many advances
have been made in our understanding of the combinatorial significance
of the nabla operator. This talk will survey recent research
in this area, beginning with the "q,t-Catalan Theorem"
of Garsia, Haglund, and Haiman and ending with a new conjectured
formula for the image of any Schur function under nabla (which
is joint work with Greg Warrington). Along the way, we will
encounter many fascinating combinatorial and algebraic entities,
including parking functions, quantum lattice paths, LLT polynomials,
diagonal harmonics modules, and Macdonald polynomials. |
| 30 Nov. 4p.m. |
York/ Fields
Combinatorics Team
Open problems - III |
| 23 Nov. 4p.m. |
York/ Fields
Combinatorics Team
Open problems - II |
| 16 Nov. 4p.m. |
York/ Fields
Combinatorics Team
Open problems - I |
| 9 Nov - 4p.m. |
Huilan
Li, York University
Representation theory of the Hecke algebra at q=0 |
| 2 Nov - 4p.m. |
Lenny
Tevlin (Yeshiva University, New York)
Noncommutative Cauchy and q-Cauchy Identities
In the talk I will try draw a parallel between the classical
theory of symmetric functions and that of noncommutative ones.
In particular there are two new bases in NSym, the
analog of monomial and fundamental bases, that allow one to
introduce an analog of the classical Cauchy identity. It appears
that in the noncommutative world both ribbon Schur and fundamental
functions are distinct analogs of classical Schur functions.
Integrality of
ribbon Schur basis in either of monomial or fundamental noncommutative
basis (which has been recently proven) requires an introduction
of what appears to be an interesting new
statistics on permutations. Therefore it seemsnatural to expect
new interesting objects to arise with q- and q,t generalizations.
However, from the point of view of the present writer the situation
with noncommutative Hall-Littlewood functions is less complete
and I will discuss existing candidates apropos a noncommutative
q-Cauchy identity. |
| 26 Oct - 4p.m. |
Francois Descouens (Fields
Institute)
Experimentations on Non-commutative symmetric functions with
MuPAD |
| 19 Oct- 4p.m. |
Mike Zabrocki (York University)
Tutorial
|
| 12 Oct- 4p.m. |
Mike Zabrocki (York University)
Analogs of k-Schur functions in NCSF |
5 Oct.- 4 p.m.
|
Mike Zabrocki (York University)
|
| 28 Sep- 3 p.m.** time change |
Nantel Bergeron (York University)
Introduction on Non-Commutative Symmetric Functions |
| 21 Sep- 4 p.m. |
Nantel Bergeron (York University)
Introduction to Non Communative Symmetric Functions |
