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SUMMARY:Xujia Chen (IAS)
DTSTART:20210517T010000Z
DTEND:20210517T020000Z
DTSTAMP:20260423T005743Z
UID:IBSCGP/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IBSCGP/14/">
 Lifting cobordisms and Kontsevich-type recursions for counts of real curve
 s</a>\nby Xujia Chen (IAS) as part of IBS-CGP weekly zoom seminar\n\n\nAbs
 tract\nKontsevich's recursion\, proved in the early 90s\, is a recursion f
 ormula for the counts of rational holomorphic curves in complex manifolds.
  For complex fourfolds and sixfolds with a real structure (i.e. a conjugat
 ion)\, signed invariant counts of real rational holomorphic curves were de
 fined by Welschinger in 2003. Solomon interpreted Welschinger's invariants
  as holomorphic disk counts in 2006 and proposed Kontsevich-type recursion
 s for them in 2007\, along with an outline of a potential approach of prov
 ing them. For many symplectic fourfolds and sixfolds\, these recursions de
 termine all invariants from basic inputs. We establish Solomon's recursion
 s by re-interpreting his disk counts as degrees of relatively oriented pse
 udocycles from moduli spaces of stable real maps and lifting cobordisms fr
 om Deligne-Mumford moduli spaces of stable real curves (which is different
  from Solomon's approach).\n
LOCATION:https://researchseminars.org/talk/IBSCGP/14/
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