Mathematical Sciences: Research on Conformal Field Theory

940841费尔德拟议活动的主要目标是明确地描述黎曼曲面上的共形块，作为微分方程组的解空间，推广Knizhnik-Zamolodchikov方程。我们将研究这些方程及其解的性质。特别是，将计算解的积分表示，并应用于曲面上的配置空间的拓扑、三维流形的不变量以及量子群和可积系统的理论。共形场理论起源于临界温度下的表面物理和弦理论，弦理论是粒子相互作用的统一模型。本研究的对象是共形场理论的数学结构。这一理论明确地将一个被称为“保形块”的复矢量空间的数学对象与模拟物理系统的方程联系在一起。***

940841 Felder The main goal of the proposed activity is to give an explicit description of conformal blocks on Riemann surfaces, as a space of solutions of a system of differential equations, generalizing the Knizhnik-Zamolodchikov equations. Properties of the equations and their solutions will be investigated. In particular, integral representations of the solutions will be calculated, with applications to the topology of configuration spaces on surfaces, invariants of three-dimensional manifolds, and the theory of quantum groups and integrable systems. Conformal Field Theory finds its origin in the physics of surface at critical temperature, and string theory, a unified model of particle interactions. The object of this research is the mathematical structure of Conformal Field Theory. This theory explicitly associates a mathematical object called a complex vector space of "conformal blocks" with equations that model physical systems. ***