Mr Nick Williams (University of Leicester) gives a maths seminar at the School of Mathematics, UEA. The talk is on “An algebraic interpretation of the higher Stasheff–Tamari orders”. The abstract is below.

The two higher Stasheff–Tamari orders generalise the well-studied Tamari lattice of triangulations of a convex n-gon to higher dimensions by considering instead the set of triangulations of a cyclic polytope. The orders were implicit in the work of Kapranov and Voevodsky, but were first defined explicitly by Edelman and Reiner, who conjectured them to be equal. Edelman and Reiner showed this to hold in low dimensions, but the general result is still unknown. Meanwhile, on the algebraic side, Oppermann and Thomas connected triangulations of even-dimensional cyclic polytopes with the tilting modules over Iyama’s higher Auslander algebras of type A. In this talk I outline recent work in which I show how the higher Stasheff–Tamari orders fit into the algebraic picture of Oppermann and Thomas. Indeed, it turns out that they coincide with higher-dimensional versions of orders on tilting modules studied by Happel, Unger, Riedtmann, and Schofield.