Seminar Event Detail


Geometry & Physics

Date:  Monday, March 11, 2019
Location:  4096 East Hall (4:00 PM to 6:00 PM)

Title:  Kontsevich-type recursions for counts of real curves

Abstract:   Kontsevich's recursion, proved by Ruan-Tian 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 Kontsevich-type recursions for them in 2007, along with an outline for adapting Ruan-Tian'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 re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves.

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Speaker:  Xujia Chen
Institution:  Stony Brook

Event Organizer:     

 

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