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 now study adiabatic theory for many body quantum systems and its application to the linear response theory (short and long). Myself, I am now interested in applications of the adiabatic theory in the context of quantum control.
OPEN QUANTUM SYSTEMS - In some way all my recent 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).