Mathematics Colloquia and Seminars

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Schur functions show up in various fields of math. If a symmetric function can be written as a non-negative sum of Schur functions, it might be counting something. The Stanley symmetric functions are such examples. I will introduce their connection with algebra (the symmetric groups), combinatorics (crystals), and geometry (cohomology of flag varieties). The K-Stanley symmetric functions are generalizations of the Stanley symmetric functions. They also lie in the intersection of algebra (the 0-Hecke monoid) and geometry (K-theory of flag varieties). The combinatorial (crystal) part of the story is missing and is what we are working on. I will explain our methods and tools, as well as our partial results.

This work is ongoing with Wencin Poh and Anne Schilling.

There will be pizza.