Lifting Lagrangians from symplectic divisors

Speaker: Luís Diogo, UFF.

Date: 01 nov 2019, 11h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: We prove that there are infinitely many non-symplectomorphic monotone Lagrangian tori in complex projective spaces, quadrics and cubics of complex dimension at least 3. This is a consequence of the following: if Y is a codimension 2 symplectic submanifold  of a closed symplectic manifold X, then we can explicitly relate the superpotential of a monotone Lagrangian L in Y with the superpotential of a monotone Lagrangian lift of L in X. This sometimes involves relative Gromov-Witten invariants of the pair (X,Y). We start by defining the superpotential, which is a count of pseudoholomorphic disks with boundary on a Lagrangian, and which plays an important role in Floer theory and mirror symmetry.

This is joint work with D. Tonkonog, R. Vianna and W. Wu.