Y-systems and generalized associahedra II

Sergey Fomin

University of Michigan

February 22,
refreshments at 3:45pm


This is the second of two talks based on a joint paper with Andrei Zelevinsky, which was motivated by the theory of cluster algebras , on one hand, and by Zamolodchikov's periodicity conjecture for Y-systems, on another.

The presentation will be self-contained, and will focus on the second part of the title ("generalized associahedra").

We introduce and study a family of simplicial complexes which can be viewed as a generalization of the Stasheff polytope (a.k.a. associahedron) for an arbitrary root system. In types A and B, our construction recovers, respectively, the ordinary associahedron and the Bott-Taubes polytope, or cyclohedron. In a follow-up joint project with Frederic Chapoton, we present explicit polytopal realizations of these generalized associahedra. On the enumerative side, these constructions provide natural root system analogues to noncrossing/nonnesting partitions.

Speaker's Contact Info: fomin(at-sign)math.lsa.umich.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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