Last updated: October 2, 2006
 
International Conference on
Representations of Algebras and
Related Topics


Northeastern University
Boston, Massachusetts

October 6 - 7, 2006


 
This conference is a follow-up to the Maurice Auslander Distinguished Lectures. Its goal is to give an opportunity to a diverse group of mathematicians attending the Lectures to exchange ideas and help establish new contacts. To register or for further information, contact Alex Martsinkovsky >alexmart >at< neu >dot< edu<.



Schedule

October 6.

    Location: 320 Behrakis

1:30 - 2:10   J. Weyman,
Semi-invariants of quivers: new developments.

2:10 - 2:30   Coffee break

2:30 - 3:10   M. Neusel,
Rings of invariants satisfying the Weak Splitting Principle.

3:30 - 4:10    D. Happel, TBA



October 7.


     Location: 315 Behrakis


9:30 - 10:10     I. Horozov, Multiple zeta functions, modular forms and iteration over the adeles.

10:30 - 11:10  
R. Schiffler, Geometric realizations of cluster categories.

11:30 - 12:10  
T. Bruestle, Cyclic cluster algebras of rank three.

2:00 - 2:40       G. Todorov, m-cluster categories

3:00 - 3:40       M. Kleiner,  Representations of quivers and the Weyl group of a Kac-Moody algebra.




Titles and Abstracts

Thomas Bruestle, Cyclic cluster algebras of rank three

Abstract: Cluster algebras, introduced by Fomin and Zelevinsky a few years ago, have gained a lot of interest by now. Acylic cluster algebras have been shown to be
related to cluster categories and tilted algebras. Cyclic cluster algebras, however, are less well understood. We consider the first non-trivial case, cluster algebras of rank three (square, coefficient-free), and study which of them are cyclic. Rank three cluster algebras are given by triples of integers (x,y,z), and we provide an answer which involves the hyperplanes defined by x2 + y2 + z2 - xyz = c.


Ivan Horozov, Multiple zeta functions, modular forms and iteration over the adeles

Abstract: Multiple zeta functions with values at the positive integers have an interpretation as iterated integrals, due to Kontsevich. We give an intepretation of multiple zeta functions with complex variables whose real part is greater than 1 as iterated integrals over the adeles. Iteration of modular forms was recently defined by Manin. We give interpretation of iterated modular forms as iteration over the adeles.


Mark Kleiner, Representations of quivers and the Weyl group of a Kac-Moody algebra

Abstract: We discuss connections between the preprojective representations of a quiver, the (+)-admissible sequences of vertices, and the Weyl group.  To each preprojective representation corresponds a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group.  As a consequence, for any Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced words.  The latter strengthens known results of Howlett and  Fomin-Zelevinsky. The talk is based on joint work with Helene R. Tyler and with Allen Pelley.


Mara Neusel, Rings of Invariants Satisfying the Weak Splitting Principle

Consider a finite group G acting linearly on the ring of polynomial functions F[V]=F[x_1,...., x_n] in n indeterminants over a field F. The associated ring of invariants F[V]^G satisfies the weak splitting principle if there exist finitely many orbits B_1,..., B_l \subseteq V* of linear forms whose Chern classes generate the ring of invariants. We present old and new results on this type of invariant rings, and some open problems.


Ralf Schiffler, Geometric realizations of cluster categories

Abstract: The cluster category of a hereditary algebra is usually defined as a quotient of the bounded derived category of modules of that algebra. In this talk, we will consider an alternative definition of the cluster categories of Dynkin types A and D. In type A, the cluster category is a category of diagonals in a regular polygon, and, in type D, the cluster category is a category of certain homotopy classes of paths in a regular polygon with one puncture in its center.


Jerzy Weyman, Semi-invariants of quivers: new developments

Abstract: This is joint work with Calin Chindris and Harm Derksen. I will explain how one can use quiver representations to find counterexamples to the  conjecture of Andrei Okunkov on the  log-concavity of Littlewood-Richardson coefficients.