Algebre cluster: un'introduzione

ARGOMENTI: Convegni Dottorato

Mercoledi` 13 febbraio 2008 alle ore 15:00, in aula 1BC/45 Giovanni Cerulli Irelli (Dottorato in Matematica Pura) "Algebre cluster: un'introduzione"

-Abstract (Cluster Algebras: an overview)
Cluster algebras were introduced in 2001 by S. Fomin and A. Zelevinsky with the aim of study total positivity and canonical basis in semi-simple algebraic groups. After their introduction, the theory has been developed in several unexpected fields of mathematics, e.g. quiver representations, Grassmannians and projective configurations, a new family of convex polytopes (generalized associahedra) including as special case Stasheff's associahedron, Al. Zamolodchikov's Y-systems in thermodinamic Bethe Ansatz, discrete dynamical system, Teichmuller spaces and Poisson geometry,etc... .
In this talk I will recall the definition of such algebraic structure and I will give some motivating examples arising from algebraic geometry. I will also try to give an idea of the connection with the previous theory with particular attention to quiver representations.

Rif. int. C. Marastoni, T. Vargiolu

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