A finitary property of particular interest to Professor Gould is that of coherency. We say that a monoid S is right coherent if every finitely generated S-subact of every finitely presented right S-act is finitely presented. Certainly right noetherian monoids are right coherent, but the converse is far from true. Coherency arises naturally from several directions, as this talk will explain. It is closely related to notions of purity, which arise from considerations of equations over S-acts, and hence to injectivity.
Professor Gould will present a selection of the results in this area and also a number of open problems.
Professor Victoria Gould was an undergraduate and a PhD student at York, then a temporary lecturer at Bristol and Manchester before holding a Royal Society European Research Fellowship at the Technishe Hochshule, Darmstadt. She returned to York with an SERC (now EPSRC) Postdoctoral Fellowship, later joining the permanent academic staff.
Her research interests are in algebra, at the abstract end: semigroup theory, universal algebra and model theory. She enjoys working with her students and other collaborators from around the world. Recently, her main projects have involved free idempotent generated semigroups, finitary properties of monoids, free partial algebras and some classical structural approaches to certain classes of non-regular semigroups.