Mathematical Sciences: Problems in Conformal Field Theory

朱克曼将研究拓扑共形场理论。他将研究在TCFT的状态空间中自然定义的代数结构。他还将研究TCFT作为一大类模型，包括共形弦背景。Khesin将继续研究Virasoro李代数和李群在一维流体动力学和二维非线性波传播中的作用。他还将继续研究与Virasoro Lie代数相关的泊松括号代数的高级类似物。现代物理学，量子力学和相对论，是二十世纪的产物。它牢固地建立在上个世纪对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础，统称为数学物理学，范围从控制粒子动力学的薛定谔算子的详细分析，到试图将四种已知力统一为单一理论的统一场论。

Zuckerman will investigate topological conformal field theory. He will study the algebraic structures that are naturally defined in the state space of a TCFT. He will also investigate TCFT as a broad class of models that include the conformal string backgrounds. Khesin will continue to investigate the role of the Virasoro Lie algebra and Lie group in one dimensional fluid dynamics and two dimensional nonlinear wave propagation. He will also pursue his study of higher analogs of the Poisson bracket algebra associated to the Virasoro Lie algebra. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.