Current Research Themes

Topics expected to be discussed include:

GEOMETRIC QUANTUM MECHANICS

1) Geometric mechanics of quantum systems: applications of Euler-Poincaré reduction to quantum and hybrid quantum/classical systems, Koopman-von Neumann theory. Nonadiabatic molecular dynamics, and its hydrodynamic description in both the mean-field and exact factorisation models. Quantisation of symplectic dual pairs, and their applications in semiclassical descriptions of quantum systems.

2) Geometry of quantum mechanics: geometric measures of entanglement. The geometry of symmetric, informationally complete positive operator valued measures (SIC-POVMs). Lindblad dynamics of Gaussian states in the semiclassical limit, and the emergence of non-Hamiltonian flow. Quantum thermodynamics and quantum coherence.

STOCHASTIC GEOMETRIC MECHANICS

1) Fluid mechanics and geophysics: uncertainty quantification and data-driven modeling of uncertainty in geometric fluid mechanics. Numerical modeling and data assimilation for stochastic Lie transport.

2) Other systems: general theory of Euler-Poincaré reduction with advected quantities. Stochastic extensions of non-holonomic constraints for mechanical systems. Perturbation to conservation laws related to group actions, stochastic averaging.

SYMMETRY AND PHYSICS

Coherent states in semiclassical descriptions of quantum systems. Non-hermitian methods for quantum systems. Entanglement in many-body quantum systems. Quantum integrable systems. Algebraic geometry in application to gauge theory.