Date & Time: Monday, March 29, 2010, 16:30-17:30.
Venue: Ramanujan Hall
Title: An Introduction to Cluster Algebras
Speaker: Javad Asadollahi, University of Isfahan
Abstract: Cluster Algebras were invented by Fomin and Zelevinsky in joint work in 2000. Their aim was to find a combinatorial approach to two theories due to G. Luszting: the theory of canonical bases in quantum group theory and theory of total positivity in algebraic groups. After that, the theory of cluster algebras has witnessed spectacular growth, according to the many links that have been discovered with a wide range of subjects including Poisson Geometry, Teichmuller spaces, integrable systems, combinatorics and the representation theory of quivers and finite dimensional algebras. In this descriptive talk, first we will discuss the notion of representation of quivers and then we will study quiver mutations and the cluster algebra associated with a quiver, following Fomin-Zelevinsky.