Hofer geometry via toric degeneration (Q6624750)

Hofer geometry, a branch of symplectic topology, uses a metric known as the Hofer metric to measure the distance between transformations in the group of Hamiltonian diffeomorphisms of a symplectic manifold. The goal of this paper, as stated by the author, is to use toric degenerations to study Hofer geometry using distinct homogeneous quasimorphisms on the group of Hamiltonian diffeomorphisms on a closed symplectic manifold. A toric degeneration generically is a process drawn from algebraic geometry created to transform a projective variety into a toric variety.\N\NThe author focuses on \(n\)-dimensional complex quadric hypersurfaces and the del Pezzo surfaces. This is in order to study two classes of Lagrangian submanifolds, ones which appear naturally with toric degenerations. A primary goal is to use toric degeneration to get new insight into Hofer geometry with a focus on real dimensions greater than 2.