From permutations to linear algebra: the Robinson-Schensted-Knuth correspondence

The Robinson-Schensted-Knuth (RSK) correspondence is a combinatorial algorithm appearing in many areas of mathematics such as probability, representation theory, algebraic geometry, and commutative algebra. For example, it plays a role in the study of longest increasing subsequences of permutations and their connections to random matrix theory.

I will introduce RSK through examples and then discuss recent joint work with Ada Stelzer in which we study RSK from another point of view: as a linear operator rather than just a bijection. This gives rise to questions about eigenvalues and diagonalizability.