Date: Monday, March 11, 2019
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Kontsevichtype recursions for counts of real curves
Abstract: Kontsevich's recursion, proved by RuanTian in the early 90s, enumerates rational curves in complex surfaces. Welschinger defined invariant signed counts of real rational curves in real surfaces (complex surfaces with a conjugation) in 2003. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevichtype recursions for them in 2007, along with an outline for adapting RuanTian's homotopy style argument to the real setting. For many symplectic fourfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by reinterpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from DeligneMumford moduli spaces of stable real curves.
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Speaker: Xujia Chen
Institution: Stony Brook
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