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SUMMARY:Martha Precup (Washington University in St. Louis)
DTSTART:20210112T190000Z
DTEND:20210112T200000Z
DTSTAMP:20260423T024027Z
UID:AG-Davis/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/15/
 ">The cohomology of nilpotent Hessenberg varieties and the dot action repr
 esentation</a>\nby Martha Precup (Washington University in St. Louis) as p
 art of UC Davis algebraic geometry seminar\n\n\nAbstract\nIn 2015\, Brosna
 n and Chow\, and independently Guay-Paquet\, proved the Shareshian--Wachs 
 conjecture\, which links the combinatorics of chromatic symmetric function
 s to the geometry of Hessenberg varieties via a permutation group action o
 n the cohomology ring of regular semisimple Hessenberg varieties. This tal
 k 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 nilpot
 ent Hessenberg varieties. As an application\, we obtain new geometric insi
 ght into certain linear relations satisfied by chromatic symmetric functio
 ns\, known as the modular law. This is joint work with Eric Sommers.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/15/
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