ADIABATIC THEORY - I learned the adiabatic theory from Yosi Avron during my postdoc in Technion. We then worked on the theory in the context of Lindblad equation (see here). Fast forward many years, with Wojciech De Roeck and Sven Bachmann we study adiabatic theory for many body quantum systems and its application to the linear response theory (short and long).
Quantum Hall Effect - In a series of recent works (integer, fractional, short) with Wojciech De Roeck, Sven Bachmann and Alex Bols we developed a many-body index theory that in particular proofs quantization of conductance in gapped intectaning systems. My current focus is on understanding the fractional quantum Hall effect.
OPEN QUANTUM SYSTEMS - In some way, most of my work falls into this category. To single out a specific work, in an article (here) with Gian Michele Graf and Yosi Avron we discuss the notion of current in Markovian open quantum systems, and describe the corresponding notion of virtual work.
QUANTUM ESTIMATION - My interest in the topic originates in trying to understand how atomic clocks work. Altough I have only two works with quantum estimation as a primary subject (here and here), it influenced my view on other topics. Going back to the study of atomic clocks is one of my main research plans.
QUANTUM TRAJECTORIES - With Miguel Ballesteros, Jürg Fröhlich and Baptiste Schubnel we are developing the topic in the context of theory of measuremnt (see here). This led us to the study of perturbation theory of non-demolitin measurements (here), that I studied previously in the context of adiabatic perturbation theory (here). With Tristan Benoist, Clément Pellegrin and Yan Pautrat we study general ergodic properties of quantum trajectories (see here).