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Positivity for cluster algebras from surfaces
Algebra & Discrete Mathematics| Speaker: | Lauren Williams, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Fri, Sep 25 2009, 4:10PM |
Description
I'll start by introducing the cluster algebras of Fomin and Zelevinsky,
then present a construction of the cluster algebra associated to a Riemann
surface with marked points (based on Fomin-Shapiro-Thurston). By work of
Felikson-Shapiro-Tumarkin, this construction realizes all but finitely many
(= eleven) of the cluster algebras of finite mutation type. Then I will
explain a combinatorial formula for the Laurent expansion of each cluster
variable in any such cluster, with respect to an arbitrary seed. An
immediate corollary of our formula is a proof of the positivity conjecture
of Fomin and Zelevinsky for cluster algebras from surfaces.
This is joint work with Gregg Musiker and Ralf Schiffler.