Summer Institute on Algebraic Geometry

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Algebraic Geometry Summer Institute (Proposal DMS-0456683.)A large scale summer institute in algebraic geometry, three weeks induration, will be held during July-August 2005 at the University ofWashington, Seattle. Organizational support will be provided by theAmerican Mathematical Society and the Clay Mathematics Institute. Eachweek will have a general topic as a focus and at the same time willinclude a component of core "classical" algebraic geometry. The foci will be: Mathematical Physics in Algebraic Geometry; Combinatorics, Commutative Algebra and Classical Algebraic Geometry; and Arithmetic AlgebraicGeometry. Three plenary morning lecture series will be held in each week, lecturers having been selected as leading researchers who are at the same time exemplary expositors. In addition, leading specialists will beinvited to serve as seminar leaders, and will select high impact lectures given by the best lecturers for afternoon seminars. Additional activities will include the CMI distinguished lectures and an evening graduateprogram.Algebraic geometry, the study of geometric shapes defined by polynomialequations, is a vast generalization of the high-school topic "analyticgeometry". It has enjoyed much cross-fertilization in past decades withareas in pure mathematics, applied mathematics, computing and theoretical physics. One way American algebraic geometers have maintained the vibrancy of the field is by holding a large scale, NSF-funded summer instituteabout every decade, an institute which aims to bring participants up tothe forefront of research in the salient direction the field has taken in the previous years, and to project directions which the field is expected to take in the following years. These institutes have had a crucialformative role on the subject, with enormous impact especially on theemerging careers of young researchers. This summer institute project aims to follow in their footsteps.