A study of RG flows in strong theory

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This proposal outlines a method of studying dynamical processes instring theory, which is one of the candidates for a theory ofquantum gravity. This is through the study of renormalization group (RG) flows,which are equations describing the flow of geometry of the space (inwhich the string propagates) under scale transformations on the world-sheettraced by the string. In an interesting connection between diverse areas ofmathematics and physics, the simplest of this class of equations was analyzed for entirelydifferent reasons by many mathematicians, including G. Perelman. There is enormous potential forgeneralizing Perelman's work to the various RG flows of string theory and understanding its implications for dynamical processes in quantum gravity.This is the main objective of this project - which I have already begun,by applying, along with collaborators, a part of Perelman's work to stringtheory.