Program in Geometry of String Theory

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AbstractAward: DMS-0443699Principal Investigator: Mikhail KapranovWe propose to run a year-long program at the Fields Institute onthe subject of ``Geometry of string theory''. The program willbe devoted to mathematical subjects motivated by string theory,and to recent developments in string theory and related physicalfields which are of strong mathematical interest. On themathematical side, the aim is to foster interaction between suchareas of mathematics as derived categories, elliptic cohomology,geometric Langlands correspondence, quantum cohomology,differential geometry varieties with special holonomy and ofspecial Lagrangian varieties. On the more physical side, the aimis to foster new progress in the continuing drive towardsunderstanding the foundations of string/M-theory, and in thewealth of new ideas involving D-branes, BPS states and variousdualities which are of great importance to mathematical subjectssuch as algebraic geometry.The overall goal of the program is to advance our understandingof the fundamental questions of physics of themicroworld. Probably the most promising application of quantumphysics contemplated nowadays is the Quantum Computing Projectwhich can potentially lead to creation of computers whose powerexceeds the present-day limits by many orders of magnitude. Thisdirection is a part of the proposed activitie and we plan to havea distinguished lecture series (the Blyth Lectures) devoted tothe subject. This program represents an excellent opportunityfor young scholars to experience a high-level interdisciplinarycollaboration. In particular, it is going to be a very importanttraining ground for young American scientists.