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SUMMARY:How a Jacobi form counts curves on Abelian surfaces and threefolds
DTSTART:20160531T151500
DTEND:20160531T170000
DTSTAMP:20260512T050010Z
UID:e635f92ea55a75a8da33b2f1f20d55f8a59e3f473adffc15985509f7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jim Bryan\, UBC\nWe explain how the solution to some natural c
 urve counting problems on Abelian surfaces and threefolds is given by the 
 Fourier coefficients of a certain Jacobi form. In the first half of the ta
 lk\, we give an elementary description of the curve counting problems and 
 we explain how their solution is elegantly given as the Fourier coefficien
 ts of a classical Jacobi form. We explain the key geometric construction t
 hat underlies the case of the surface. In the second part of the talk\, we
  delve deeper into curve counting on an Abelian threefold via Donaldson-Th
 omas theory. We explain how a combination of motivic and toric methods lea
 ds to a computation of the Donaldson-Thomas invariants in terms of the top
 ological vertex. The Jacobi form then emerges via a new and surprising tra
 ce identity which expresses the vertex in terms of Jacobi forms.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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