Travel Support: Infinite Dimensional Lie Algebras, Quantum Groups and their Applications

拟议的项目是支持伯克利的8名研究生前往丹麦奥胡斯的模空间量子几何中心。研究生将参加研究工作坊，参加大师班和其他研究活动，并与欧洲同行一起工作。研究主题位于表示理论和数学物理的交汇点。更具体地说，它针对1的根处的量子群表示理论中的问题，关于3-流形的不变量的问题，局部量子场论中的某些问题(例如微扰的Chern-Simons理论的构造)，以及可积系统中的问题和统计力学的可解模型。建立基本相互作用模型是现代理论物理的核心问题之一，它与实验相一致，并且在数学上是充分的。局域量子场论的框架是标准模型背后的主要概念。然而，量子场论的框架在很大程度上仍然是一个数学难题。部分研究将集中在半经典量子化的背景下理解这个谜题。提案的其他部分的目标是组合地构建拓扑和可积量子场论，以及研究新出现的代数和分析问题。

The proposed project is to support eight graduate students in Berkeley to travel to the Center for Quantum Geometry of Moduli Spaces in Aarhus, Denmark. Graduate students will participate in research workshops, attend master-classes and other research activities as well as to work together with their peers in Europe.The research topics lie at the interface of representation theory and mathematical physics. More specifically, it aims at problems in the representation theory of quantum groups at roots of 1, on invariants of 3-manifolds, certain problems in local quantum field theory (such as the construction of perturbative Chern-Simons theory), and on problemsin integrable systems and solvable models of statistical mechanics. One of the central questions in modern theoretical physics is the construction of the model of fundamental interaction which is consistent with experiment and mathematically adequate. The framework of local quantum field theory is the main concept behind the standard model. However the framework of quantum field theory still largely remains a mathematical puzzle. Part of the research will focus on understanding this puzzle in the context of semi-classical quantization. The goal of other parts of the proposal is the construction of topological and integrable quantum field theories combinatorially and the study of emerging algebraic and analytical problems.