Olivetti Club
Tuesday, September 12, 2023 - 4:35pm
Malott 406
In this talk, I will explain why I've spent the last two years telling acquaintances that my research involves designing colorful puzzle games. The Grassmannian is the space of k-dimensional subspaces of an n-dimensional space; it is an example of a beautiful type of structure called a cluster algebra. Postnikov gave a combinatorial description of certain coordinates for the Grassmannian using dimers (matchings) on plabic graphs, and Marsh-Scott linked this description to an automorphism called the twist map. To twist higher-degree cluster variables, we can enumerate overlays of certain sets of dimers based on rules that are surprisingly visual and natural to describe.