Minicourses

Abstract: Introduced by D. E. Littlewood in 1936, plethysm is a fundamental operation on symmetric functions, originally motivated by representation theory. Plethystic calculus is an extension of the plethysm operation which has become an indispensable computational tool in the theory of Macdonald symmetric functions. 

In the first two lectures, we introduce symmetric functions and plethystic calculus, showing how to use them to derive a few interesting identities in Enumerative and Algebraic Combinatorics. In the third and last lecture we will present a few open problems, some classical and some more recent.

This minicourse has virtually no prerequisites, but it will be full of "manipulatorics" (copyright Adriano Garsia): participants discretion is advised.