IAS/Park City Mathematics Institute Mathematics Research Component

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This project is a continuation, for the years 2004-2009, of the mathematics programs of the Institute for Advanced Study/Park City Mathematics Institute (PCMI). Three programs, the Research Program, the Graduate Summer School and the Undergraduate Summer School, are organized around a single area of contemporary mathematical research, which varies from year to year.Mathematical topics and organizers for 2004-08 are in place. All programs take place for a three-week period each July in a conference center in Park City, Utah. Led by world-renowned mathematicians as lecturers and lead researchers, each of the three programs requested in this proposal has 30-70 participants.Over the last 13 years, PCMI (with its predecessor, the NSF-funded Regional Geometry Institute) has established itself as the national summer school in advanced mathematics, uniquely integrating undergraduate study, graduate study, and mathematical research activities via concurrent and integrated programs of study and research.