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A_infty structures in open Gromov-Witten theory


Speaker: Sara Tukachinsky, MSRI
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Location: 2112 MSB
Start time: Tue, Apr 24 2018, 1:10PM

In 2003, Welschinger defined invariants of real symplectic manifolds of complex dimensions 2 and 3, which are related to counts of pseudo-holomorphic disks with boundary and interior point constraints (Solomon, 2006). The problem of extending the definition to higher dimensions remained open until recently (Georgieva, 2013, and Solomon-Tukachinsky, 2016).

An obstruction to invariance is bubbling of disks at the boundary. In this talk I will explain the problem, and define an A_infty algebra associated to a Lagrangian submanifold, following ideas of Fukaya-Oh-Ohta-Ono (2009) and Fukaya (2011). This A_infty algebra serves as a language for tracking pseudo-holomorphic disks and bubbling. We then introduce an associated Maurer-Cartan equation, whose solutions allow a definition of invariants in a suitable sense (an idea demonstrated by Joyce, 2006).