Conférencier: Nick Williams,Lancaster University

Abstract:Cyclic polytopes are a very special family of polytopes possessing some beautiful properties. In particular, the set of triangulations of a cyclic polytope has a rich combinatorial structure which appears in several other areas of mathematics. This set of triangulations possesses two natural partial orders, which can be seen as generalisations of the Tamari lattice. These are known as the first and second higher Stasheff--Tamari orders, the first of which was introduced by Kapranov and Voevodsky, and the second introduced by Edelman and Reiner. Edelman and Reiner conjectured these two orders to coincide. In this talk we outline our proof of this conjecture. This result also has ramifications for the representation theory of certain finite-dimensional algebras, which we will touch on if time permits.