Exactly Solving Physical Systems: Methods and Applications

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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.