Last week we learned that skew Schur functions are Schur-positive. After a quick review, we will ask when the difference of two skew Schur functions is Schur positive, i.e., when is s_A - s_B Schur-positive for skew shapes A and B? It will be helpful to address this question in the following setting: make the set of all skew shapes into a partially ordered set by saying that B is less than or equal to A if s_A - s_B is Schur-positive. Our goal is to study this partially ordered set. My three most recent research projects all fall into this framework. I will present one slide each on two of these projects before looking more deeply at the third.

Two of these projects are joint work with Stephanie van Willigenburg

The slides in pdf (recommended), ps, ps.gz.