Speaker: Andrew Sack (UCLA)

Title: The combinatorics of poset associahedra

Abstract:  For a poset $P$, Galashin introduced a simple polytope $\mathscr A(P)$ called the $P$-associahedron. We will discuss a simple realization of poset associahedra and show that the $f$-vector of $\mathscr A(P)$ depends only on the comparability graph of $P$. Furthermore, we will show that when $P$ is a rooted tree, the 1-skeleton of $\mathscr A(P)$ orients to a lattice, answering a question of Laplante-Anfossi. These lattices naturally generalize both the weak order on permutations and the Tamari lattice. This is joint work with Colin Defant and Son Nguyen.