Titles and Abstracts
Thomas Brustle, Surface triangulations and string combinatorics
Abstract: To every triangulation T of an oriented surface without
punctures one can associate a string algebra A(T). We study properties
of these algebras and their representations. This talk is based on
joint work with I. Assem, G. Charbonneau and P-G. Plamondon.
Calin Chindris, Orbit semigroups and the representation type for quivers
Abstract: Orbit semigroups of quiver representations arise
naturally in the construction of GIT-fans for quivers. By
Derksen-Weyman saturation theorem for semi-invariants, we know that
orbit semigroups are saturated for generic representations. However, there are quiver representations
whose orbit semigroups fail to be saturated. In this talk, we show that
a finite connected quiver is a Dynkin or Euclidean quiver if and only
if the orbit semigroups of all quiver representations are saturated.
François Huard, Finitistic dimension through infinite projective dimension
Abstract: This is joint work with M. Lanzilotta and O. Mendoza.
We show that an artin algebra with at most three radical layers of
infinite projective
dimension has finite finitistic dimension. This generalizes
the known result for algebras with vanishing radical cube.
In order to achieve our goal, we use the Ψ-function of Igusa and
Todorov and introduce the notion of "infinite-layer length" which
counts in a natural manner the number of (not necessarily radical)
layers of infinite projective dimension of a finitely generated module
over an artin algebra.
Colin Ingalls, Spaces of Linear Modules on Regular Graded Clifford algebras
Abstarct: The space of regular noncommutative algebras includes regular
graded Clifford algebras, which correspond to base point free linear
systems of quadrics in dimension $n$ in $P^n$. The schemes of
linear modules for these algebras can be described in terms of this
linear system. We show that the space of line modules on a 4
dimensional algebra is an Enriques surface called the Reye congruence,
and we extend this result to higher dimensions.
Shiping Liu, Auslander-Reiten theory in a Krull-Schmidt category
Abstract: N/A
Mara Neusel, Permutation Groups and Invariant Theory
Abstract: Let $\rho : G\hookrightarrow GL(n, F)$ be a faithful
representation of a finite group. It induces (after a choice of dual
basis) an action of the group $G$ on the ring of polynomial functions
$\F[x_1, ... x_n]$ in $n$ variables. In this talk we are focusing on
representations such that $\rho(G)\leq \Sigma_n$ consists of
permutation matrices. We show that the classical dichotomy between
nonmodular-modular representations is not quite relevant for
permutation representations. In particular, we prove an old conjecture
saying that the regular representation is, in some sense, the worst.
Charles Paquette, Homological Properties of Strictly Stratified Algebras
Abstract: Strictly stratified algebras were introduced by Agoston, Dlab
and Lukacs. This class of algebras generalizes the well-known
class of standardly stratified algebras. In this talk, we will
study, by means of the Ext functors, the finitistic (injective)
dimension of such algebras. We will also look at the self
extensions of simple modules and at the Cartan determinant of strictly
stratified algebras.
Ralf Schiffler, A Cluster Expansion Formula
Abstract: We will present a formula for the Laurent expansions of
cluster variables that holds for cluster algebras which are associated
to unpunctured surfaces. The formula is given in terms of certain paths
on a given triangulation of the surface.