Title: Framing lattices and flow polytopes
Abstract: In this talk we introduce a vast new family of lattices which we call "framing lattices". They arise from directed acyclic graphs and encompass many combinatorially interesting lattices, including the Boolean lattice, the Tamari lattice, type A cambrian lattices, the weak order of the symmetric group, along with many of their recent generalizations. Framing lattices are also intimately tied to the geometry of triangulated flow polytopes. We will discuss this geometric connection along with known structural results regarding framing lattices. Many examples will be explored throughout the talk. This talk is based on joint work with Cesar Ceballos.