Quantised lattices and combinatorics

Abstract:

Quantised lattices, or q-lattices, appear naturally through categorification constructions - for example from "zigzag-algebras" - but they haven't been studied from a lattice theory point of view. After establishing the necessary background, we'll explain the "q-versions" of various lattice theory concepts and results, illustrated with examples from combinatorics and graph theory. We'll also list a number of open problems. (With Tony Licata and Leo Jiang.)