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SUMMARY:Megumi Harada (McMaster University)
DTSTART:20220428T185000Z
DTEND:20220428T195000Z
DTSTAMP:20260423T022916Z
UID:GPRTatNU/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/43/
 ">Hessenberg patch ideals\, geometric vertex decomposition\, and Grobner b
 ases</a>\nby Megumi Harada (McMaster University) as part of Geometry\, Phy
 sics\, and Representation Theory Seminar\n\n\nAbstract\nHessenberg varieti
 es are subvarieties of the flag variety $Flags(\\mathbb{C}^n)$\, the study
  of which have rich interactions with symplectic geometry\, representation
  theory\, and equivariant topology\, among other research areas\, with par
 ticular recent attention arising from its connections to the famous Stanle
 y-Stembridge conjecture in combinatorics. The special case of regular nilp
 otent Hessenberg varieties has been much studied\, and in this talk I will
  describe some work in progress analyzing the local defining ideals of the
 se varieties. In particular\, using some techniques relating liason theory
 \, geometric vertex decomposition\, and the theory of Grobner bases (follo
 wing work of Klein and Rajchgot)\, we are able to show that\, for the coor
 dinate patch corresponding to the longest word $w_0$\, the local defining 
 ideal for any indecomposable Hessenberg variety is geometrically vertex de
 composable\, and we find an explicit Grobner basis for a certain monomial 
 order. This is a report on joint work in progress with Sergio Da Silva.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/43/
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