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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2013-StG
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Host institution
91904 JERUSALEM
Israel
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.