Although algebraic in nature, symmetric functions have long been of considerable interest in combinatorics. We will begin with a general introduction to the combinatorics of symmetric functions, where the two main highlights will be the Schur functions and the Littlewood-Richardson rule. Much of the appeal of Schur functions stems from their appearance in other areas of mathematics, and we will mention connections with representation theory, algebraic geometry (Schubert calculus, in particular) and matrix theory.
This will prepare us for the second half of the talk, where we will discuss cylindric Schur functions. As well as being a natural generalization of Schur functions, they are of much relevance to a fundamental open problem in algebraic combinatorics.
No knowledge of symmetric functions or combinatorics will be assumed.