# Conference

ARTA III Advances in Representation Theory of Algebras

The third Advances in Representation Theory of Algebras (ARTA) meeting will be held at the Université du Québec à Montréal, Montréal, Québec, Canada, from the 16th to the 20th of June 2014.

# Announcements

Winter 2014

## Thematic semester : New Directions in Lie Theory

Many postdoctoral positions are available through the CRM during the thematic semester New Directions in Lie Theory held from january to june 2014.

# News

Friday, November 28, 2014

## titre à venir

Vincent Pilaud, CNRS & École Polytechnique

résumé à venir

Friday, December 05, 2014

## Initial-seed recursions and dualities for $d$-vectors (Joint with Nathan Reading)

Salvatore Stella, NCSU

abstract: Cluster variables in a cluster algebra can be parametrized by two families of integer vectors: $d$-vectors and $g$-vectors. While $g$-vectors satisfy two recursive formulas (one for initial-seed-mutations and one for final-seed-mutations), $d$-vectors admit only a final-seed-mutation recursion. We present an initial-seed-mutation formula for $d$-vectors and give two rephrasings of this recursion: one as a duality formula for $d$-vectors in the style of the $g$-vectors/$c$-vectors dualities of Nakanishi and Zelevinsky, and one as a formula expressing the highest powers in the Laurent expansion of a cluster variable in terms of the $d$-vectors of any cluster containing it. We will show that the initial-seed-mutation recursion holds in a varied collection of cluster algebras, but not in general. We conjecture further that the formula holds \emph{for source-sink moves on the initial seed} in an arbitrary cluster algebra, and show that this conjecture holds the case of surfaces.

Friday, December 05, 2014

## Pattern avoiding Polyominoes

Andrea Frosini, Université de Florence

abstract: The concept of pattern within a combinatorial structure is an essential notion in combinatorics, whose study has had many developments in various branches of discrete mathematics. Among them, the research on permutation patterns and pattern-avoiding permutations has become very active. Nowadays, these researches have being developed in several other directions, one of them concerning the definition and the study of an analogue concept in other combinatorial objects. Some recent studies are presented here, concerning patterns in bidimensional structure, and, specifically, inside polyominoes. After introducing polyomino classes, i present an original way of characterizing them by avoidance constraints (namely, with excluded submatrices) and i discuss how canonical such a description by submatrix-avoidance can be. I also provide some examples of polyomino classes defined by submatrix-avoidance, and i conclude with some hints for future research on the topic.

Friday, December 12, 2014

## On the asymptotics of Kronecker coefficients

Laurent Manivel, CNRS

résumé: Kronecker coefficients are the structure constants for tensor products of Specht modules, the irreducible complex representations of symmetric groups. They can be computed with combinatorial tools, but I will explain how they can be approached by geometric methods. This is very efficient in order to understand their asymptotics, in particular their stability properties.

Friday, January 09, 2015

## titre à venir

Jean-Philippe Labbé, Einstein Institute of Mathematics

résumé à venir