# Counting holomorphic disks using bounding chains

Speaker
Sara Tukachinsky, Princeton University
Date
10/06/2018 - 13:15 - 12:15Add to Calendar 2018-06-10 12:15:00 2018-06-10 13:15:00 Counting holomorphic disks using bounding chains   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, 2016-17).   In the talk I will give some background on the problem, and describe a generalization of Welschinger's invariants to higher dimensions, with boundary and interior constraints, a.k.a. open Gromov-Witten invariants. This generalization is constructed in the language of $A_\infty$-algebras and bounding chains, where bounding chains play the role of boundary point constraints. If time permits, we will describe equations, a version of the open WDVV equations, which the resulting invariants satisfy. These equations give rise to recursive formulae that allow the computation of all invariants of $\mathbb{C}P^n$ for odd $n$.   This is joint work with Jake Solomon.   No previous knowledge of any of the objects mentioned above will be assumed. Mathematics Colloquium Room 201, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Mathematics Colloquium Room 201, Building 216
Abstract

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, 2016-17).

In the talk I will give some background on the problem, and describe
a generalization of Welschinger's invariants to higher dimensions,
with boundary and interior constraints, a.k.a. open Gromov-Witten
invariants. This generalization is constructed in the language of
$A_\infty$-algebras and bounding chains, where bounding chains play
the role of boundary point constraints. If time permits, we will
describe equations, a version of the open WDVV equations, which the
resulting invariants satisfy. These equations give rise to recursive
formulae that allow the computation of all invariants of
$\mathbb{C}P^n$ for odd $n$.

This is joint work with Jake Solomon.

No previous knowledge of any of the objects mentioned above will be assumed.

תאריך עדכון אחרון : 06/06/2018