Physically Inspired Mathematics Seminar – Marco Castronovo

Curved Fukaya algebras and the Dubrovin spectrum

Abstract: The cohomology ring of a compact symplectic manifold can be deformed by counting pseudo-holomorphic spheres. Fukaya-Oh-Ohta-Ono developed an obstruction theory that explains when Lagrangian submanifolds yield modules over such deformation, based on counting pseudo-holomorphic disks. I will focus on a piece of numerical data coming out of their theory and called curvature, explaining why it must be an eigenvalue of an operator studied by Dubrovin much earlier. I will also outline how this could simplify the calculation of the Fukaya category of G/P.

Physically Inspired Mathematics Seminar