Algebraic and Enumerative combinatorics seminar -Scott Neville-Eventual sign coherence

Abstract: The sign coherence of c-vectors is one of the fundamental theorems of cluster algebras with principal coefficients.  Gekhtman and Nakanishi posed the Asymptotic Sign Coherence Conjecture for cluster algebras with arbitrary coefficients, which says sign coherence should eventually hold in any sufficiently generic infinite mutation sequence.  We prove that for cluster algebras from quivers of arbitrary rank, their conjecture holds with probability 1 for a random mutation sequence.  Our results also establish the conjecture in full generality for many families of quivers.  This is joint work with Amanda Burcroff.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.