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SUMMARY:Arnav Tripathy (Stanford University)
DTSTART;VALUE=DATE-TIME:20211001T190000Z
DTEND;VALUE=DATE-TIME:20211001T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T081334Z
UID:agstanford/66
DESCRIPTION:Title: Line bundles in equivariant elliptic cohomology\nby Arnav Tripathy
(Stanford University) as part of Stanford algebraic geometry seminar\n\n\
nAbstract\nGiven a compact Lie group G acting on a space X\, the G-equivar
iant elliptic cohomology of X is naturally a scheme Ell_G(X) (with a map d
own to the moduli space of G-bundles on elliptic curves). Given a G-equiva
riant vector bundle V on X\, one obtains an interesting line bundle Thom(V
) on Ell_G(X). Both topologists and string theorists have predicted that g
iven two vector bundles V_1\, V_2 whose first Chern classes both vanish an
d whose second Chern classes agree\, the resulting line bundles Thom(V_1)
and Thom(V_2) should agree in Pic(Ell_G(X)). I'll describe how the theory
of pushforwards in topology gives rise to this subtle question in algebrai
c geometry\, and I hope to indicate in broad strokes the proof of this con
jecture. This is joint work with D. Berwick-Evans.\n
LOCATION:https://researchseminars.org/talk/agstanford/66/
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