Conference Proposal: Developments in Algebraic Geometry

这是一项为期一天的代数几何会议的提议，会议将于2007年6月2日在密苏里州普罗维登斯市的布朗大学举行。会议将聚焦于当前令人兴奋的数学发展，其起源可以追溯到大卫·芒福德的工作。预计将有80-120人参加会议，其中博士后和研究生45-60人。2007年6月1日在国际扶轮纽波特为纪念David Mumford而举办的视觉和神经科学研讨会的一些参与者也将参加会议。Mumford的工作帮助形成了大量的代数几何。直到今天，仍有许多广泛的领域仍然受到他的影响。这次会议将有五次口语式讲座，每一次都介绍我们在一个代数几何领域的理解现状，并提出仍然存在的有趣的开放问题。五位演讲者和他们的主题是：(I)V.Alexeev(乔治亚大学)：几何不变理论，代数簇的稳定性，向量丛的稳定性。(Ii)I.Krichever(哥伦比亚大学)：交换簇中雅可比簇的刻画(肖特基问题)。(Iii)M.Rapoport(波恩大学)：交换簇和p-可分群的模。(Iv)V.Shokurov(约翰霍普金斯大学)：高维代数簇的分类，以及正则环的有限生成。(V)U·蒂尔曼(牛津大学)：曲线的模空间的拓扑。通过将在不同领域工作的人们以及研究生和职业生涯早期的研究人员聚集在一起，我们希望推动这些重要领域的进步和创新。预计将产生相当广泛的影响：会议将为年轻研究人员提供一个论坛，让他们与资深科学家讨论他们的工作，并为纯粹的数学家与视觉科学家交流思想。这次会议也得到了克莱数学研究所的支持。

This is a proposal for a one-day conference on algebraic geometry, to be held at Brown University, Providence, RI, on June 2, 2007.It will focus on the current, exciting developments in mathematics whose origin goes back to the work of David Mumford. It is expected that 80-120 participants will attend the conference, including 45-60 postdocs and graduate students. Some participants of a workshop on vision and neuroscience in honor of David Mumford, at Newport, RI on June 1, 2007, will also attend the conference.Mumford's work helped shape a huge swath of algebraic geometry. There are many broad fields which remain dominated by his influence to this very day.There will be five colloquium-style lectures in this conference, each giving an account of our present state of understanding in one area of algebraic geometry, and present the fascinating open problems that remain.The five speakers and their topics are:(i) V. Alexeev (University of Georgia): geometric invariant theory, stability of algebraic varieties, stability of vector bundles.(ii) I. Krichever (Columbia University): characterization of Jacobian varieties among abelian varieties (the Schottky problem).(iii) M. Rapoport (University of Bonn): moduli of abelian varieties and p-divisible groups.(iv) V. Shokurov (Johns Hopkins University): the classification of higher dimensional algebraic varieties, and the finite generation of the canonical ring.(v) U. Tillmann (Oxford University): the topology of the moduli space of curves.By bringing together people who work in diverse areas, as well as graduate students and early-career researchers, we hope to promote progress and innovation in these important fields. Considerable broader impact is expected:the conference will provide a forum for young researchers to discuss their work with senior scientists, and for pure mathematicians to exchange ideas with vision scientists.This conference is also supported by the Clay Mathematics Institute.