Automorphisms and deformations of regular semisimple Hessenberg varieties

Regular semisimple Hessenberg varieties are smooth subvarieties in flag varieties which have interesting nontrivial symmetric group actions on their cohomology. In this talk, we discuss their automorphisms and deformations, when they are divisors in the flag varieties. Especially in type A, we provide a complete classification, along with an interpretation in terms of pointed rational curves, and describe the moduli stack of such Hessenberg varieties as a quotient stack of the moduli space of pointed rational curves. This is a joint work with P. Brosnan, L. Escobar, J. Hong, E. Lee, A. Mellit and E. Sommers.