Valley Geometry Seminar

摘要“山谷几何研讨会”(DMS-9703485)这笔赠款的目的是支持山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、微分拓扑学、算术几何学、几何拓扑学及相关领域。我们的主要活动是由当地演讲者或来自其他学院和大学的专家每周进行的一系列演讲。在某些学期，研讨会将集中在一个专题上。在接下来的学期中，我们可能会探讨的主题包括朗兰兹计划、环变簇和镜面对称，以及实代数几何。山谷几何研讨会的参与者来自阿默斯特学院、芒特霍利奥克学院、史密斯学院和马萨诸塞大学。研讨会的目的是让在不同几何领域工作的当地数学家有机会向同情他们的同行的听众讲述他们最近的工作。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中至关重要的一部分。此外，我们还安排了研讨会，使演讲真正有用。我们鼓励演讲者做两个部分的演讲，中间有短暂的休息，而不是通常的一小时演讲。第一部分包括动机和例子--研讨会成员可以看到正在讨论的主题如何适应当代研究的更大框架的“大图景”。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，还必须能够给出无懈可击的证明。因此，第二部分是对会谈第一部分的必要补充。我们发现这种格式非常有用，我们的大多数演讲者都采用这种格式。最后，有些学期我们专注于一个特定的主题。这意味着会谈的一些(但不是全部)涉及同一主题的各个方面。这样，我们对这个话题的理解才能真正深入。

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.