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).
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).