Mathematical Aspects of String Theory

A small sampling of such interaction would include the development of the theory of partial differential equations, geometry and the theory of gravity, non-Abelian gauge theories and fiber bundles, anomalies, supersymmetry and the index theorem, and instantons and Donaldson's theorem. We are fortunate to again be in a time when we can actively support this kind of interaction. The development of quantum string theories by physicists requires knowledge from many branches of mathematics. The mathematics that is required for the further development of string theory provides a rich source of mathematical problems to solve.