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SUMMARY:Martha Precup (Washington University)
DTSTART:20201019T200000Z
DTEND:20201019T210000Z
DTSTAMP:20260423T021506Z
UID:UMassRep/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMassRep/5/"
 >The cohomology of nilpotent Hessenberg varieties and the dot action repre
 sentation</a>\nby Martha Precup (Washington University) as part of UMass A
 mherst Representation theory seminar\n\n\nAbstract\nIn 2015\, Brosnan and 
 Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs conjec
 ture\, which links the combinatorics of chromatic symmetric functions to t
 he geometry of Hessenberg varieties via a permutation 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 numbers of certain nilpotent He
 ssenberg varieties. As an application\, we obtain new geometric insight in
 to certain linear relations satisfied by chromatic symmetric functions\, k
 nown as the modular law. This is joint work with Eric Sommers.\n
LOCATION:https://researchseminars.org/talk/UMassRep/5/
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