Cluster expansions, snake graphs, and continued fractions

Hanna Mularczyk
Massachusetts Institute of Technology
Mathematics

Abstract: By the celebrated Laurent phenomenon, we can express any cluster variable of a cluster algebra as a Laurent polynomial in the initial seed variables with integer coefficients. How can we explicitly, directly calculate these Laurent polynomials? How many terms do these polynomials have? We will answer these questions, focusing on type A, with work from Canakci, Musiker, Schiffler, Williams, and others.


Back to Geometry, Statistical Mechanics, and Integrability