Topics on Hessenberg varieties

Hessenberg varieties are subvarieties of flag varieties. Recently, it turned out that their topology makes connections with other research areas, such as logarithmic derivation modules in hyperplane arrangements and chromatic symmetric functions in graph theory. In this talk, I will explain their connections. Also, if time permits, then I would like to talk about a recent result of a connection between Hessenberg varieties and some toric orbifolds. This talk is based on three joint works with H.Abe-M.Harada-M.Masuda, T.Abe-M.Masuda-S.Murai-T.Sato, M.Masuda-J.Shareshian-J.Song.