I am interested in emergent collective behaviour of quantum (and classical) systems that consist of a large number of constituents that exchange information with each other (i.e. interact). Some examples of these phenomena I worked on are quantum Hall effect, fracton excitations in various systems, hydrodynamics of electron flows and of active systems, solitons in nonlinear systems, analogue Hall effect in optical systems and others. More recently I became interested in theoretical foundations of deep learning, namely the emergent collective behaviour in deep neural networks.
In my research I often use the tools of quantum and classical field theory, hydrodynamics, Riemann, Newton-Cartan and non-commutative geometry.