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Title: Dubronvin dynamics

Abstract: The cohomology ring of a compact symplectic manifold can be deformed by counting pseudo-holomorphic spheres, and this categorifies by considering disks. I will raise a question, make a proposal, do a calculation, and prove a theorem. Question: why do we focus on certain points in the space of deformations? Proposal: study cohomological/categorical properties that hold for generic deformation parameters. Calculation: the eigenvalues of Dubrovin’s operator are distinct for all parameters of P^2, and coalesce for non-generic parameters of Gr(2,4). Theorem: the Dubrovin spectrum contains the curvatures of nontrivial objects in the Fukaya category.