BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Evgeny Feigin (National Research University Higher School of Econo
 mics)
DTSTART:20201002T150000Z
DTEND:20201002T160000Z
DTSTAMP:20260423T024740Z
UID:LieTheory/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LieTheory/1/
 ">Veronese embeddings\, arc schemes and global Demazure modules</a>\nby Ev
 geny Feigin (National Research University Higher School of Economics) as p
 art of CRM-Regional Conference in Lie Theory\n\nLecture held in Virtual.\n
 \nAbstract\nVeronese curve of degree d (also known as rational normal curv
 e) can be realized as an embedding of the complex projective line into a d
 -dimensional projective space.  The equations cutting out the image of thi
 s embedding can be written down explicitly and the homogeneous coordinate 
 ring has an explicit description in terms of representations of the comple
 x Lie algebra sl(2). To pass to the corresponding arc scheme\, one replace
 s the field of complex numbers with the ring of formal Taylor series in on
 e variable. We describe the reduced ideal of the arc scheme and the homoge
 neous coordinate ring in terms of representation theory of the current alg
 ebra of sl(2).\nThe whole picture generalizes to the case of an arbitrary 
 simple Lie algebra.  The analogues of the rational normal curves are the V
 eronese embeddings of the flag varieties for the corresponding Lie group. 
 We identify the homogeneous coordinate ring of the reduced arc scheme of t
 he Veronese embedding with the direct sum of the global Demazure modules o
 f the current algebra  (the higher level analogues of the global Weyl modu
 les).  Joint work with Ilya Dumanski.  Geometric flows of $G_2$ and Spin(7
 )-structures\n
LOCATION:https://researchseminars.org/talk/LieTheory/1/
END:VEVENT
END:VCALENDAR