9502965 Adler The proposed research aims to give a mathematical formulation of string theory. The investigator proposes to work on the string equation and its discrete analogs: these equations are related to matrix models, KP-hierarchy and W-algebras. The proposed research will use the Duistermaat-Heckman integral (Fourier transform of the Liouville measure of a symplectic manifold with a group action) to evaluate matrix integrals arising in the string equation. String theory provides a global model for the universe encompassing Einstein's general theory of relativity. And this research is an attempt to lay a rigorous mathematical foundation for it.
