| |
The goal of this research is to develop geometric tools to study and classify supersymmetric theories, in particular superconformal field theories in string theory, as its non-perturbative extensions, M- and F-theory. Underlying these questions is a mathematical structure, the Higgs bundle, which characterizes supersymmetric vacua of dimensionally reduced gauge theories, and insights into the moduli space of Higgs bundles will result in a fruitful cross-connection geometry and quantum field theories. |