Floer Thoery

Floer theory is a symplectic extension to Morse theory which concerns itself with critical points of an (action) functional, such as Hamiltonian orbits. In particular, it can be used to find cuplength estimates: topological lower bounds to the number of periodic Hamiltonian solutions. Floer theory is also important in (developments in) homological mirror symmetry, topological quantum field theory and low-dimensional (especially 3- and 4-dimensional) topology.

Quantum Mechanics

We aim to extend Floer theory, which is inherently classical, to quantum mechanics. The ultimate goal is to improve our understanding of quantum mechanics using dynamical methods, instead of the ordinarily used eigenstate methods. We have thus far been able to apply Floer theory to stochastic electrodynamics, a classical approximation of quantum electrodynamics which is exact up to first order in \(\hbar\).