04/02/2020, 15:00 — 16:00 — Room P3.10, Mathematics Building
Luís Diogo, Universidade Federal Fluminense, Brasil
Lifting Lagrangians from symplectic divisors
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 will define 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.