Sergey Fomin, U. of Michigan
Cluster complexes of bordered surfaces

To an oriented surface with boundary and finitely many marked points one can associate a simplicial complex (indeed, a pseudomanifold), namely, the cluster complex of the corresponding cluster algebra. I will present a self-contained description of this complex in terms of the combinatorial topology of [the triangulations of] the surface; give examples, which include associahedra of types A and D; and state some proven and conjectural properties of cluster complexes.

No background on cluster algebras is required. This is joint work with Michael Shapiro and Dylan Thurston.