Quiver mutation and derived equivalence


Tuesday 29 April 2008 at 11:30, room 2BC/60, Torre Archimede
Bernhard Keller (professor at Paris 7)
"Quiver mutation and derived equivalence"

[The seminar will be divided in two parts of 40' each, the first of which, of introductory type, will be suitable for a large public]

1. In the first part, we will define and study quiver mutation. This is an elementary operation on quivers (=oriented graphs) which was introduced by Fomin and Zelevinsky in the definition of cluster algebras at the beginning of this decade. The combinatorics behind quiver mutation are rich and varied. We will illustrate them on numerous examples using computer animations.
2. In the second part of the talk, we will "categorify" quiver mutation using representation theory. More precisely, by combining recent work of Derksen-Weyman-Zelevinsky and Ginzburg, we will show how quiver mutations give rise to equivalences between derived categories of certain differential graded algebras. These derived categories are closely related to cluster categories and thus to cluster algebras.
This is joint work with Dong Yang.

Rif. int. C. Marastoni, T. Vargiolu

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