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SUMMARY:Sean Griffin (University of Washington)
DTSTART:20200520T200000Z
DTEND:20200520T210000Z
DTSTAMP:20260423T040151Z
UID:AG-Davis/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/4/"
 >Springer fibers\, rank varieties\, and generalized coinvariant rings</a>\
 nby Sean Griffin (University of Washington) as part of UC Davis algebraic 
 geometry seminar\n\n\nAbstract\nSpringer fibers are a family of varieties 
 with the remarkable property that their cohomology rings $R_\\lambda$ have
  the structure of a symmetric group module\, even though there is no $S_n$
  action on the varieties themselves. This is one of the first examples of 
 a geometric representation. In the 80s\, De Concini and Procesi proved tha
 t $R_\\lambda$ has another geometric description as the coordinate ring of
  the scheme-theoretic intersection of a nilpotent orbit closure with diago
 nal matrices. This led them to an explicit presentation for $R_\\lambda$ i
 n terms of generators and relations\, which was further simplified by Tani
 saki. In this talk\, we present a generalization of this work to the coord
 inate ring of a scheme-theoretic intersection of Eisenbud-Saltman rank var
 ieties. We then connect these coordinate rings to the generalized coinvari
 ant rings recently introduced by Haglund\, Rhoades\, and Shimozono in thei
 r work on the Delta Conjecture from Algebraic Combinatorics. We then give 
 combinatorial formulas for the Hilbert series and graded Frobenius series 
 of our coordinate rings generalizing those of Haglund-Rhoades-Shimozono an
 d Garsia-Procesi.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/4/
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