Title: Semigroups of valuations on local rings

Abstract: Although the possible value groups that dominate a noetherian local ring are well understood, very little is known about the semigroups of values actually attained on the local ring. We begin by reviewing the classical theory, and then give a number of methods of producing examples, which indicate that there may be no restrictions on the semigroups which can be attained besides those known classically. This talk is on joint work with Bernard Teissier.