species and combinatorial Hopf algebras on the one hand, and quantum groups and the classification theory of abstract Hopf algebras on the other. This is part of joint work with Swapneel Mahajan. MAHIR CAN, University of Western Ontario Bruhat Orders and Combinatorics on Reductive Monoids Originating from the early '80s, the theory of reductive monoids is a combinatorial, fledgling branch of algebraic geometry within the theory of spherical embeddings. It brings together algebraic groups, the torus embeddings and semigroups. One can (na