Exactly Solving Physical Systems: Methods and Applications

我的研究重点是精确地解决物理模型。它关系到量子信息完美传输的系统设计。它研究了用于开发量子计算算法的量子行走。它研究了在从生物聚合到交通流量等各种领域都具有相关性的不对称排除过程。它还着眼于遗传学建模中感兴趣的随机过程。我的研究计划的很大一部分也致力于那些被称为可积或超可积的系统，因为它们有许多守恒量。它们在理论上很重要，并且有很多应用。基本的方法论是基于对对称性的研究。我参与了它们在代数结构、正交多项式和特殊函数方面的数学描述的发展。

My research focuses on exactly solving physical models. It bears on the design of systems for the perfect transport of quantum information. It examines quantum walks that are used to develop algorithms for quantum computing. It studies asymmetric exclusion processes that are of relevance in a variety of fields ranging from biopolymerization to traffic flow. It looks also at stochastic processes of interest in genetics modeling. A significant part of my research program is also devoted to systems that are called integrable or superintegrable because they have many conserved quantities. They are theoretically important and have many applications. The underlying methodology is based on the study of symmetries. I am involved in the development of their mathematical description in terms of algebraic structures and orthogonal polynomials and special functions.