|DATE||July 03 (Fri), 2020|
|TITLE||The cohomology rings of regular Hessenberg varieties I|
Hessenberg varieties form a distinguished class of closed subvarieties in the flag variety, and this class includes all Grothendieck--Springer fibres, the Peterson variety, and the projective toric variety associated to the Weyl chambers. Several important results and conjectures in algebraic combinatorics amount to statements about the cohomology rings of regular Hessenberg varieties. My first lecture will develop this idea, providing the relevant background on Hessenberg varieties in the process. The second lecture will outline some recent joint work with Ana Balibanu on Hessenberg varieties and their cohomology rings.