In addition to having rich internal properties, ordered structures such as posets, lattices and lattice-ordered groups have applications in logic, topology and graph theory.
One area of our research is concerned with dualities, such as the Stone duality and the Priestley duality.
We are interested in topological spaces and their properties from a point-free perspective, utilizing the frames (lattices where finite meets distribute over arbitrary joins) of open sets.
We also study prohibited configurations, or posets, that characterize various topological spaces and objects. The prototypical example is Kuratowski's characterization of planar graphs as those that do not contain a subgraph which is a subdivision of K5 or K3,3.