Abstracts

Andrei Zelevinsky: Quivers with potentials and their representations
This is an account of an ongoing joint work with Harm Derksen and Jerzy Weyman. We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This gives a far-reaching generalization of Bernstein-Gelfand-Ponomarev reflection functors. The motivations for this work come from several sources: superpotentials in physics, Calabi-Yau algebras, cluster algebras.

Dave Benson: Modules of constant Jordan type
Let E be an elementary abelian p-group and k an algebraically closed field of characteristic p. A kE-module is said to be of constant Jordan type if its restriction to every element of J(kE)\J^2(kE) has the same Jordan canonical form. I shall describe some recent work giving restrictions on the possible Jordan types, and work with Pevtsova on vector bundles on projective space associated with modules of constant Jordan type.

Martin Rubey: Partially directed self avoiding walks in a wedge and nestings of matchings and permutations
We present a simple bijective proof of the fact that matchings of [2n] with N nestings are equinumerous to partially directed self avoiding walks confined to the symmetric wedge defined by y=\pm x, with n east steps and N north steps. A very similar construction connects permutations with N nestings and PDSAWs remaining below the x-axis, again with N north steps. Furthermore, both bijections transport several combinatorially meaningful parameters.