Mathematics Colloquium- Ricky Liu, University of Washington

Title: Plane partitions and rowmotion

 

Abstract: Plane partitions are two-dimensional analogues of partitions that have a rich history in combinatorics, with applications ranging from representation theory to statistical mechanics. After discussing some classical results on enumeration of plane partitions, we will define an action on plane partitions called rowmotion and study its dynamical properties. In particular, we will show how a birational version of rowmotion is closely related to the Dodgson condensation method for computing determinants, and we will use it to derive a surprising correspondence between plane partitions of rectangular and trapezoidal shape. This is joint work with Joe Johnson.