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Rank 2 Non-commutative Laurent Phenomenon and Positivity

SPEAKER: Dylan Rupel

TITLE: Rank 2 Non-commutative Laurent Phenomenon and Positivity

ABSTRACT Rank 2 cluster algebras are defined recursively using a pair of binomial exchange relations. In this talk I will generalize this construction in two directions. I will work in the fully non-commutative setting and consider polynomial generalizations of the exchange relations. I will present a combinatorial description of the resulting “cluster variables” which establishes a Laurent phenomenon and positivity for certain polynomial exchanges.