Mathematics faculty and graduate students are invited to attend the PhD
Preliminary Examination of Kyle Salois.

Advisor:  Dr. Maria Gillespie

Committee:  Dr. Alexander Hulpke, Dr. Renzo Cavalieri, Dr. Dongzhou Huang

Title:  Higher Specht Polynomials and Tableaux Bijections for Hessenberg Varieties

Abstract:  The cohomology rings of regular semisimple Hessenberg varieties is only understood completely in some cases. One such case is when the Hessenberg function is h=(h(1),n,…,n), and is described by Abe, Horiguchi, and Masuda in 2017. We define an alternative basis for the cohomology ring in this case, which is a higher Specht basis. We
give combinatorial bijections between the monomials in this basis and sets of P-tableaux, motivated by the work of Gasharov, illustrating the connections between the symmetric group action on these cohomology rings and the Schur expansion of chromatic symmetric functions.