Mathematical Sciences: Geometric Structure of Conformal Field Theories

本研究涉及的几何结构， 共形场论 首席研究员将研究 以下主题：（1）二叉树和李括号;（2） 行列式线丛和顶点算子代数;（3）a 两个以上扭曲元素对偶性的几何证明; (4)有限的几何定义的抽象形式 维李代数、顶点算子代数及更高维 维量子场论;（5）求幂顶点 算子代数;（6）顶点算子的幂运算 代数和椭圆上同调 该研究支持关注的一个重要焦点， 当前的数学活动，其中群表示理论， 量子场论和代数几何学结合在一起。 这项工作对理论物理学具有重要意义， 以及数学的几个领域。

This research is concerned with the geometric structure of conformal field theory. The principal investigator will study the following topics: (1) binary trees and the Lie bracket; (2) determinant line bundles and vertex operator algebras; (3) a geometric proof of duality for more than two twisted elements; (4) an abstract form of the geometric definitions of finite dimensional Lie algebras, vertex operator algebras and higher dimensional quantum field theory; (5) exponentiating vertex operator algebras; (6) exponentiations of vertex operator algebras and elliptic cohomology. The research supported concerns an important focus of current mathematical activity, where group representation theory, quantum field theory, and algebraic geometry all come together. This work has important implications for theoretical physics, as well as several areas of mathematics.