Abstract for "Valley Geometry Seminar" (DMS-9703485) The purpose of this grant is to support the activities of the Valley Geometry Seminar. We interpret "geometry" broadly to include algebraic geometry, differential geometry, symplectic geometry, differential topology, arithmetic geometry, geometric topology, and related areas. Our principal activity is a weekly series of talks given by local speakers or experts from other colleges and universities. Some semesters, the seminar will concentrate on a special topic. Possible topics we will pursue in coming semesters include the Langlands program, toric varieties and mirror symmetry, and real algebraic geometry. The participants in the Valley Geometry Seminar come from Amherst College, Mount Holyoke College, Smith College, and the University of Massachusetts. The purpose of the seminar is to give local mathematicians working in different areas of geometry the chance to speak about their recent work to an audience of sympathetic peers. Also, by bringing in outside experts, we get to hear about recent developments in geometry. The seminar is a crucial part of the research atmosphere for the geometers in our area. Also, we have structured the seminar so that the talks are really useful. Rather than the usual one-hour lecture, we encourage speakers to give a two-part talk, separated by a short break. The first part consists of motivations and examples-the seminar members get to see the "big picture" of how the topic being discussed fits into the larger framework of contemporary research. The second part of the talk then gives the technical details, for in mathematics, you not only have to discover something interesting, but you also have to be able to give an airtight proof. Hence the second part is a necessary complement to the first part of the talk. We find this format very useful and most of our speakers adopt this format. Finally, some semesters we concentrate on a specific topic. This means that some (but not all) of the talks conc ern aspects of the same topic. In this way we can get some real depth in our understanding of the topic.
