Mathematical Sciences: Yang-Baxter Operators, Quantum Field Theories and Invariants in Low-Dimensional Topology via HopfAlgebras and Representations of Monoidal Categories

耶特将探索最近发现的低维拓扑学、统计力学、量子场论、霍普夫代数和么半范畴理论之间相互作用的几个方面。特别是，他将使用Hopf代数和范式论技术来构造并分类1)量子杨-巴克斯特方程的解，2)拓扑和共形量子场论。即使是部分结果，也将阐明新发现的经典纽结和链环的多项式不变量的含义和相互关系。

Yetter will explore several aspects of the recently discovered interactions between low-dimensional topology, statistical mechanics, quantum field theory, Hopf algebra and monoidal category theory. In particular, he will use Hopf algebra and category theoretic techniques to construct and, if possible, classify 1) solutions to the quantum Yang-Baxter equation and 2) topological and conformal quantum field theories. Even partial results would shed light on the meaning and interrelations of the newly discovered polynomial invariants of classical knots and links.