Combinatorics / Harvard Seminar

SPEAKER:  Julianna Tymoczko  (Smith College)

TITLE:  Hessenberg varieties, combinatorial constructions of equivariant cohomology, and the Stanley-Stembridge conecture

ABSTRACT:

The elementary symmetric functions form a well-known basis for the entire space of symmetric functions. The conjecture that the chromatic symmetric function of any (3+1)-free poset can be written as a nonnegative linear combination of elementary symmetric functions is often called the Stanley-Stembridge conjecture. We describe recent progress towards proving the Stanley-Stembridge conjecture that uses a combinatorial representation of a geometric object called a Hessenberg variety.