Quantised lattices and combinatorics

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 open problems on the q-lattice and categorical level. (With Tony Licata and Leo Jiang.)