There are many interesting subvarieties of the (partial) flag varieties including Schubert, Hessenberg and Lusztig varieties, which play important roles in representation theory and combinatorics. I will talk about an elementary geometric proof of the Shareshian-Wachs conjecture and its generalization which relate the cohomology of Hessenberg varieties with chromatic quasi-symmetric functions. Based on a joint work with Donggun Lee.