Title: Closed subset of root systems and regular subalgebras
Abstract: We describe recent work on classifying closed subsets of roots system, and on the related topic of classifying regular subalgebras of semisimple Lie algebras. In particular, we classified the closed subsets of the irreducible root systems of ranks 3 through 7, up to conjugation by the associated Weyl group. We then employed this root system classification to classify all regular subalgebras of the rank 3 simple Lie algebras, up to inner automorphism. This is joint work with Willem de Graaf.