The Stanley-Stembridge conjecture is a longstanding and famous conjecture in combinatorics. Recent research indicates that Hesenberg varieties are intimately connected to this conjecture and we have already produced preliminary results that further develop this connection. This project aims to prove the full Stanley-Stembridge conjecture using Hessenberg techniques.
Impact
A proof of the Stanley-Stembridge conjecture would have significant consequences for combinatorics as well as other research areas, particularly the geometry of flag varieties and associated representation theory.
Student Experience
Some postdoctoral fellows are involved in this project.
