Staircase diagrams and the enumeration of smooth affine permutations

Back in the 90's,  Mark Haiman calculated the generating function for permutations avoiding the smooth patterns 4231 and 3412 by studying the fiber bundle structure of  Schubert varieties of type A.  In this talk, I will discuss joint work with William Slofstra where we use similar ideas to enumerate affine permutations that avoid the same smooth patterns.