NWO M-1 grant for Oliver Fabert

The Dutch Research Council (NWO) has awarded Oliver Fabert an Open Competition Domain Science M-1 grant for his research project “Floer theory for stochastic Hamiltonian systems, quantum theory, and imaginary time”, worth 350,000 Euros for 4 years to fund one PhD position. Hamiltonian Floer theory and pseudoholomorphic curves are well-established elliptic methods in symplectic geometry. Traditionally applied to problems from classical physics, this proposal seeks to extend their utility to quantum physics through stochastic Hamiltonian systems. While stochastic electrodynamics aims at explaining quantum effects directly through the existence of a random background field, other stochastic approaches to quantization rely on the observation that the Schrödinger equation can be viewed as a diffusion-type equation in imaginary time. Passing further from quantum mechanics to quantum field theory, the Minkowski space-time becomes Euclidean and the hyperbolic wave equation turns into the elliptic Laplace equation. This project aims at generalizing the standard elliptic methods of symplectic geometry to stochastic Hamiltonian systems, with the goal of making them applicable to questions in quantum theory.