Conference Proposal: Developments in Algebraic Geometry

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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.