Algebraic Combinatorics Seminar - Colin Defant

Title: Semidistrim Lattices

Abstract:

This talk will introduce semidistrim lattices, which generalize semidistributive lattices and trim lattices; these two families, in turn, generalize distributive lattices. We will discuss structural, topological, and dynamical properties of semidistrim lattices. In particular, we will see how one can define a certain bijective operator on a semidistrim lattice called rowmotion; this definition unifies the definition that Barnard gave for semidistributive lattices and the definition that Thomas and Williams gave for trim lattices. Somewhat surprisingly, rowmotion for semidistrim lattices is intimately connected with a noninvertible operator called pop-stack sorting, which can be defined for any lattice. This talk is based on joint work with Nathan Williams.