Toric varieties and cluster algebras

Speaker:

G. Koshevoy

Affiliation:

Russian Acad. of Sciences/MPI

Date:

Thu, 2012-04-26 15:00 - 16:00

Location:

MPIM Lecture Hall [2]

Parent event:

MPI-Oberseminar [3]

We associate a toric variety to the cluster algebra of the coordinate ring of GL_n/P
(P is a parabolic subgroup). If such a cluster algebra is finite, then we have a smooth
toric variety. Our conjecture is that this holds in general.To confirm this conjecture
we construct a smooth toric variety for a framed acyclic quiver and study relations
between these two constructions of toric varieties.