Geometri- och topologiseminarium: Lifting Lagrangians from Donaldson-type divisors
- Plats: Ångströmlaboratoriet
- Föreläsare: Luis Diogo
- Kontaktperson: Maksim Maydanskiy
Abstract: Given a closed symplectic manifold with a symplectic submanifold of codimension 2, we can sometimes lift monotone Lagrangians from the submanifold to the ambient manifold. We show that under some assumptions, it is possible to write the superpotentials of the lifted Lagrangians in terms of the superpotentials of the original Lagrangians (we may also need additional information coming from relative Gromov-Witten invariants). The superpotential of a Lagrangian is a count of pseudoholomorphic disks (of Maslov index 2) with boundary on the Lagrangian, and it plays an important role in Floer theory and mirror symmetry.
We will discuss applications of this result, including how it can be used to distinguish infinitely many monotone Lagrangian tori in complex projective planes, quadrics and cubics of complex dimension at least 3. This is joint work with D. Tonkonog, R. Vianna and W. Wu.