Wednesday, January 22 at 2:00pm to 2:50pm
Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089
Nate Bottman, USC
Abstract: I will explain my construction of the 2-associahedra, which are graded posets indexed by sequences of nonnegative integers. The 2-associahedra arose in symplectic geometry, where they control functoriality for a symplectic invariant called the Fukaya category. The elements of a 2-associahedron correspond to the degenerations in the compactified configuration space of marked points on vertical lines in R^2, up to translations and positive dilations. I will explain several properties of the 2-associahedra: they are abstract polytopes (in particular, they are thin and strongly connected); they are Eulerian lattices (joint with my student Dylan Mavrides); and they have an operad-like structure that makes it possible to compute the (flag)-f-vectors using generating function techniques. I will discuss the conjecture that the 2-associahedra can be realized as convex polytopes. This will be a combinatorics talk; in particular, I will assume no symplectic background.