Atomic Clocks
Atomic clocks are one of the few commercially used quantum devices. At the moment the best atomic clocks reached precision of 10^(-18). Can this precision improve further? Is there any fundamental limit for their accuracy?
Quantum Trajectories
Quantum trajectories is a fast growing topic in mathematical-physics originating in quantum optics. It is a (somewhat singular) Markov process on the complex projective space. I am working on the topic in a large collaboration with colleagues in France, Mexico and Switzerland.
Quantum Hall Effect
A fascinating mix of topology, analysis and quantum mechanics. Thousands of people work on this topic for the last 40 years and not slowing down. I am working on the topic with Wojciech De Roeck (KU Leuven) and Sven Bachmann (UBC).