symmetric functions

Jan 07 2025

Hikita’s proof of the Stanley-Stembridge Conjecture

Mathematical Gemstones

In this arXiv paper, Hikita recently posted a proof of the famous Stanley-Stembridge conjecture! I went through the proof with my Advanced Combinatorics class, and wrote up lecture notes here: Lecture Notes on Stanley-Stembridge Part I Lecture Notes on Stanley-Stembridge Part II which I will...

diamond gemstones symmetric functions combinatorics

Mar 11 2024

The Springer Correspondence Part IV: Affine Springer Fibers

Mathematical Gemstones

I have written about the flag variety, the Springer resolution, and the relation between the type A Springer correspondence and Hall-Littlewood polynomials in a previous sequence of posts. Time to extend this construction to the (type A) affine flag variety, corresponding to affine Lie type...

representation theory diamond gemstones symmetric functions algebraic geometry