In the intersection of algebra, combinatorics, algebraic geometry and more, are functions called skew Schur functions. These functions are invaluable in translating problems from one area to another in order to make them more accessible. For example, going from algebra to combinatorics, “When are two skew Schur or Weyl modules equivalent over C?” becomes “When are two skew Schur functions equal?”, which becomes “When are two pictures of boxes the same?”
In this talk we'll attack the former by studying the latter. More precisely, we'll introduce skew Schur functions pictorially before determining conditions under which these pictures are “the same”, and then see where else in combinatorics these conditions arise.
No prior knowledge of any of the above is required.
This is joint work with Vic Reiner and Kris Shaw.