Pure Maths Colloquium - The average size of simultaneous core - Dr Paul Johnson (Sheffield) Seminar

Event details

Abstract: Although t-core partitions originally arose in the study of the representation theory of the symmetric group over fields of finite characteristic, they've since been studied from the point of view of combinatorics, number theory, and geometry. It was only in 2002 that Jaclyn Anderson began the study of partitions that were simultaneous t-core and s-core, and the study of simultaneous core partitions has really only caught in the last decade as Armstrong and collaborators connected them to rational Catalan combinatorics. This talk is a leisurely introduction to t-core partitions. There's an end goal of explaining how I recently proved Armstrong's conjecture about the average size of simultaneous core partitions by using Ehrhart theory, but we'll pause along the way to take in some of the attractions, including a quick dip into Dirac's electron sea for Borcherd's proof of Jacobi's triple product formula.