Valley Geometry Seminar

摘要“谷几何研讨会”（DMS-9703485）的目的是支持谷几何研讨会的活动。 我们广义地解释“几何”包括代数几何、微分几何、辛几何、微分拓扑、算术几何、几何拓扑和相关领域。 我们的主要活动是每周一次由当地演讲者或来自其他学院和大学的专家进行的系列讲座。 有些学期，研讨会将集中在一个特殊的主题。 未来学期可能的主题包括朗兰兹纲领、复曲面与镜像对称，以及真实的代数几何。山谷几何研讨会的参与者来自阿默斯特学院、霍利奥克山学院、史密斯学院和马萨诸塞州大学。 研讨会的目的是让本地数学家在不同领域的几何工作的机会谈论他们最近的工作，以观众的同情同行。 此外，通过引入外部专家，我们可以听到几何学的最新发展。 研讨会是我们地区几何学家研究氛围的重要组成部分。 此外，我们已经组织了研讨会，使会谈真正有用。 与通常的一小时讲座不同，我们鼓励演讲者进行两部分的演讲，中间有短暂的休息。 第一部分由动机和例子组成研讨会成员可以看到正在讨论的主题如何融入当代研究的更大框架的“大画面”。 演讲的第二部分给出了技术细节，因为在数学中，你不仅要发现一些有趣的东西，而且还要能够给出一个无懈可击的证明。 因此，第二部分是对第一部分的必要补充。 我们发现这种格式非常有用，我们的大多数发言者都采用这种格式。 最后，有些学期我们集中在一个特定的主题。 这意味着一些（但不是全部）会谈涉及同一主题的各个方面。 这样我们就能对这个话题有真实的深入的理解。

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.