BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Martha Precup (Washington University at St. Louis) DTSTART:20210204T195000Z DTEND:20210204T205000Z DTSTAMP:20260423T010133Z UID:GPRTatNU/15 DESCRIPTION:Title: The cohomology of nilpotent Hessenberg varieties and the dot action repr esentation\nby Martha Precup (Washington University at St. Louis) as p art of Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstrac t\nIn 2015\, Brosnan and Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs conjecture\, which links the combinatorics of chromatic symmetric functions to the geometry of Hessenberg varieties via a permuta tion group action on the cohomology ring of regular semisimple Hessenberg varieties. This talk will give a brief overview of that story and discuss how the dot action can be computed in all Lie types using the Betti numbe rs of certain nilpotent Hessenberg varieties. As an application\, we obtai n new geometric insight into certain linear relations satisfied by chromat ic symmetric functions\, known as the modular law. This is joint work wit h Eric Sommers.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/15/ END:VEVENT END:VCALENDAR