The University of Michigan Combinatorics Seminar


Abstract 

We present noncommutative generalizations of discrete integrable systems that possess the positive Laurent property. This is motivated by a Laurent positivity conjecture of M. Kontsevitch, regarding a noncommutative version of rank two cluster algebras, for which we give a proof in the affine cases. Our solution uses a noncommutative generalization of the path models used to solve classical Q and T systems. More generally, we will show how to use the theory of quasideterminants of Gelfand et al to define noncommutative mutations within the path model framework, as local rearrangements of noncommutative branching continued fractions. This is joint work with Rinat Kedem. 