Representation-theoretic approaches to several problems in probability theory

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The project aims to solve some problems in probability using techniques from algebra, in particular the branch called representation theory. The current problem is called the Manhattan problem, because it is based on a grid that resembles the one-way streets in Manhattan. This problem is probabilistic, but we can formulate it in terms of an algebraic object, which we name the Manhattan algebra. The project studies this Manhattan algebra, and others similar to it. In particular, we conjecture that the representation theory of the Manhattan algebra will be useful in solving the Manhattan problem.