Representation-theoretic approaches to several problems in probability theory

该项目旨在利用代数技术解决概率中的一些问题，特别是称为表示理论的分支。目前的问题被称为曼哈顿问题，因为它是基于类似于曼哈顿单行道的网格。这个问题是概率性的，但我们可以用一个代数对象来表述它，我们称之为曼哈顿代数。该项目研究曼哈顿代数，以及其他类似的代数。特别地，我们推测曼哈顿代数的表示理论将有助于解决曼哈顿问题。

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.