ECI Colloquiums

The Brauer-Thrall Conjectures, now theorems, were originally formulated in terms of representations of finite-dimensional algebras. They say, roughly speaking, that failure of finite representation type entails the existence of lots of indecomposable representations of large dimension. These conjectures have been successfully transplanted to the representation theory of commutative local rings. This talk will be a survey of such results, conjectures and counterexamples, for various categories of finitely generated modules over a commutative Noetherian local ring. The emphasis will be on maximal Cohen-Macaulay modules over Cohen-Macaulay local rings.

Colloquium: Algebraic Microlocal Analysis

To any sheaf F on a real manifold M, one associates its singular support SS(F ), a closed conic co-isotropic subset of the cotangent bundle T *M, similarly as one associates its characteristic variety char(M ) to a coherent D-module M on a complex manifold X.
In this talk, I will explain the notion of microsupport of sheaves (with many examples), describe its functorial properties and give some applica­tions to linear PDE and also, if times allows it, to symplectic topology.

ECI COLLOQUIUM

Thursday, June 28, 2pm, room K3

Gena Puninski

(Belarus State University, Minsk)

Pure injective modules over string algebras

Classic works of Gelfand-Ponomarev and Butler- Ringel have described all finite dimensional representations of string algebras.

Attempts at extending the classification to pure-injective representations have led Ringel to formulate a conjecture in the domestic case, saying that the indecomposable pure injective representations are completely determined by two kinds of combinatorial data, called bands and strings.

Puninski has recently proved this conjecture in the 1-domestic case. In the ECI Colloquium talk, he will present a general introduction to representation theory of string algebras as well as the main ideas of his proof of Ringel’s conjecture.

ECI COLLOQUIUM

Tuesday, March 27, 2pm, room K3

Alexander Zuevsky

(Max-Planck-Institute, Bonn)

Vertex operator superalgebras on sewn Riemann surfaces and modular forms

We show how to construct and calculate explici-tely the partition and n-point correlation functions for vertex operator superalgebras on
Riemann surfaces of genus g \ge 1. Twisted elliptic functions, genus two Jacobi triple product formulas  and generalized Fay's trisecant identities appear naturaly as applications of this algebraic procedure in analytic number theory and algebraic geometry.