University of Minnesota Combinatorics Seminar: 2020-2021

Date: 02/19/2021

Speaker: Sylvester Zhang

$T$-path Formula for Decorated Super-Teichmüller Spaces
Penner's $\lambda$-lengths of a decorated Teichmüller space on a marked disk form a type $A$ Cluster algebra, and recently, a supersymmetric version of the decorated Teichmüller theory was introduced by Penner and Zeitlin. In this talk, I will investigate the super $\lambda$-lengths coming from a marked disk, and give a combinatorial formula extending Schiffler's $T$-path formula for Type $A$ Cluster algebras. I will discuss the connection between the super $\lambda$-lengths and super frieze patterns of Morier-Genoud--Ovsienko--Tabachnikov. And lastly, I will also discuss how our formula relates to cluster superalgebras, a notion which is still only partially understood. This talk is based on joint work with Gregg Musiker and Nick Ovenhouse.

$T$-path Formula for Decorated Super-Teichmüller Spaces

Penner's $\lambda$-lengths of a decorated Teichmüller space on a marked disk form a type $A$ Cluster algebra, and recently, a supersymmetric version of the decorated Teichmüller theory was introduced by Penner and Zeitlin. In this talk, I will investigate the super $\lambda$-lengths coming from a marked disk, and give a combinatorial formula extending Schiffler's $T$-path formula for Type $A$ Cluster algebras. I will discuss the connection between the super $\lambda$-lengths and super frieze patterns of Morier-Genoud--Ovsienko--Tabachnikov. And lastly, I will also discuss how our formula relates to cluster superalgebras, a notion which is still only partially understood. This talk is based on joint work with Gregg Musiker and Nick Ovenhouse.