This award supports a visit by Dr. Peter R. Jones of Marquette University to the University of Tasmania, in Hobart, to work with Dr. Peter G. Trotter on an area of number theory involving semigroups. The investigators plan to merge two areas of semigroup theory research which have seen the greatest advances over the past decade, but whose development has been almost completely independent. The first is "finite" semigroup theory, which arises from the explicit connections among formal languages, automata and finite semigroups. The other is the theory of completely regular semigroups--those which are unions of their subgroups, and research on which has seen a resurgence of late. Important recent developments in each field will be applied to the other, notably Polak's decomposition theory for varieties will be applied to finite semigroup theory, and the "derived category" of a morphism will be applied to completely regular semigroup theory. The key fusion will involve a systematic study of the "local" varieties of completely regular monoids.
