Mathematical Sciences: Geometric Analysis

小行星9502965 拟议的研究旨在给出弦理论的数学公式。研究人员建议研究弦方程及其离散类似物：这些方程与矩阵模型、KP-族和W-代数相关。拟议的研究将使用Duistermaat-Heckman积分（具有群作用的辛流形的Liouville测度的傅立叶变换）来评估弦方程中产生的矩阵积分。 弦论提供了一个包含爱因斯坦广义相对论的宇宙整体模型。本文的研究试图为它奠定一个严密的数学基础。

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.