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Real and open Gromov-Witten theory

Objective

This proposal focuses on establishing new relations between natural objects in symplectic geometry with other fields of mathematics including knot and representation theory and the theory of integrable systems. All of these relations are motivated by theoretical physics. The main objects of study are moduli spaces of pseudo-holomorphic maps giving rise to real and open Gromov-Witten invariants. The classical Gromov-Witten invariants were introduced by Gromov at the birth of symplectic topology giving rise to obstructions to symplectic embeddings. Their interpretation by Witten as the coefficients of a partition function of a field theory placed them in a new light : striking dualities understood in physics relate them to mathematical objects of completely different nature and on completely different manifolds. This has and continues to generate enormous amount of high-level research aimed at understanding these relations better.

The proposed research concerns establishing such relations in the context of the recently introduced, by the PI and A. Zinger, real Gromov-Witten theory. In particular, it aims to determine the systems of differential equations governing the real Gromov-Witten theory, that parallel the KdV and Toda hierarchies in the classical case. We will further study the real Gromov-Witten theory of toric Calabi-Yau threefolds with the aim of establishing a connection with SO/Sp Chern-Simons theory and a real version of the remodeled mirror symmetry. Finally, we will seek to establish foundational results of open Gromov-Witten theory in a general context.

Call for proposal

ERC-2019-COG
See other projects for this call

Host institution

SORBONNE UNIVERSITE
Address
21 Rue De L'ecole De Medecine
75006 Paris
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 351 375

Beneficiaries (1)

SORBONNE UNIVERSITE
France
EU contribution
€ 1 351 375
Address
21 Rue De L'ecole De Medecine
75006 Paris
Activity type
Higher or Secondary Education Establishments