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Symplectic topology and its interactions: from dynamics to quantization

Final Report Summary - SYMPTOPODYNQUANT (Symplectic topology and its interactions: from dynamics to quantization)

The project addresses a number of challenges in Symplectic Topology, a rapidly developing
mathematical discipline providing basic tools for modeling a variety of fundamental physical
processes. I advanced understanding of the quantum-classical correspondence
and studied an interplay between Symplectic Topology and Quantum Mechanics. In particular,
I discovered and explored various facets of a link between displacement energy, a fundamental topological invariant, and the universal quantum speed limit (with L. Charles). I developed symplectic methods for detecting instabilities in Classical Mechanics and applied it to fast drift in Hamiltonian systems (with M. Entov). I introduced a new symplectic technique based on the ideas of Topological Data Analysis with applications to geometry and dynamics of systems of Classical Mechanics (with E. Shelukhin).