OPENGWTRIANGLE

Three ideas in open Gromov-Witten theory

Coordinatore	THE HEBREW UNIVERSITY OF JERUSALEM.    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Israel [IL]
Totale costo	1˙249˙000 €
EC contributo	1˙249˙000 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2013-StG
Funding Scheme	ERC-SG
Anno di inizio	2013
Periodo (anno-mese-giorno)	2013-10-01   -   2018-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	THE HEBREW UNIVERSITY OF JERUSALEM.  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Dr. Nome: Jake P. Cognome: Solomon Email: send email Telefono: +972 2 6584187 Fax: +972 2 5630702	IL (JERUSALEM)	hostInstitution	1˙249˙000.00
2	THE HEBREW UNIVERSITY OF JERUSALEM.  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Ms. Nome: Hani Cognome: Ben-Yehuda Email: send email Telefono: +972 2 6586676 Fax: +972 7 22447007	IL (JERUSALEM)	hostInstitution	1˙249˙000.00

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 Obiettivo del progetto (Objective)

'The questions motivating symplectic geometry, from classical mechanics to enumerative algebraic geometry, have been studied for centuries. Many recent advances in the field have stemmed from the theory of J-holomorphic curves, and in particular Gromov-Witten theory. The past 25 years of research have produced a fairly detailed picture of what can be expected from classical, closed Gromov-Witten theory. However, closed Gromov-Witten theory by itself lacks an interface with Lagrangian submanifolds, one of the fundamental structures of symplectic geometry. The nascent open Gromov-Witten theory, in which Lagrangian submanifolds enter as boundary conditions for J-holomorphic curves, provides such an interface. The goal of the proposed research is to broaden and systematize our understanding of open Gromov-Witten theory. My strategy leverages three connections with more established fields of research to uncover new aspects of open Gromov-Witten theory. In return, open Gromov-Witten theory advances the connected fields and reveals links between them. First, the closed and open Gromov-Witten theories are intertwined. Representation theoretic structures in closed Gromov-Witten theory admit mixed open closed extensions. Further, real algebraic geometry gives rise to a large variety of Lagrangian submanifolds providing an important source of intuition for open Gromov Witten theory. In return, open Gromov-Witten theory techniques advance Welschinger's real enumerative geometry. Finally, open Gromov-Witten theory plays a key role in mirror symmetry, a conjectural correspondence between symplectic and complex geometry originating from string theory. In particular, open Gromov-Witten invariants appear in the construction of mirror geometries. Moreover, under mirror symmetry, Lagrangian submanifolds correspond roughly to holomorphic vector bundles. Well understood functionals associated to holomorphic vector bundles go over to open Gromov-Witten invariants.'