**Abstract:**

The associahedron is a well-known polytope with connections to many different areas of combinatorics, algebra, geometry, topology, and physics. The associahedron has Catalan number many vertices which can be equivalently described in terms of triangulations of a polygon, planar binary trees, maximal parenthesizations of a word, etc. From one perspective, the associahedron encodes the combinatorics of morphisms in the Fukaya category of a symplectic manifold. In 2017, Bottman introduced a family of posets called 2-associahedra which encode the combinatorics of functors between Fukaya categories, and he conjectured that they can be realized as the face posets of convex polytopes. In this talk, I will begin by reviewing the basic theory of associahedra. I will then introduce n-associahedra as a natural extension of associahedra and 2-associahedra, and I will produce a family of complete polyhedral fans called velocity fans whose face posets are the n-associahedra. This is joint work with Nathaniel Bottman and Daria Poliakova.

**Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.**

**Join Zoom Meeting: https://washington.zoom.us/j/ 91547335974Meeting ID: 915 4733 5974**