John Shareshian:
Hessenberg varietes and combinatorics

Hessenberg varieties are subvarieties of flag varieties that were studied closely first by De Mari and Shayman and then by De Mari, Procesi and Shayman.  These varieties have been of interest to applied mathematicians, representation theorists, geometers, and combinatorialists. 

I will describe some old and new results on Hessenberg varieties in which familiar combinatorial objects appear.