Symplectic Picard-Lefschetz theory

Speaker: Hossein Movasati, IMPA.

Date: 05 jul 2019, 15h30.

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

Abstract: Is it possible to classify all homological cycles of a given symplectic manifold supported in Lagrangian spheres? The question in this generality might be ambiguous and too difficult. However, for complex projective varieties endowed with the Fubini-Study metric, Lefschetz vanishing cycles turn out to be supported in Lagrangian spheres and the monodromy action on them gives us a big class of such homological cycles. In this talk, I will report on a partial result in this direction for a family of Calabi-Yau threefolds called mirror quintic. The talk is partially based on my book 'A course in Hodge Theory: With Emphasis on multiple integrals' and Daniel Lopes Ph.D. thesis.