The group is currently doing research in condensed matter theory, quantum quantum nonlinear dynamics (``quantum chaos''), and nonequilibrium systems. Below's a very brief exposure of our current research activities:
nonlinear dynamics: we are applying path integral and field theoretical methods to understand universal phenomena in quantum systems that have a chaotic classical limit. Examples of such systems include ballistic semiconductor systems ('quantum billiards'), periodically driven systems, or weakly disordered electronic systems. At low energies, or large time scales, the physical properties of chaotic quantum systems become fully universal. In this regime, they can be modeled by phenomenological theories, such as random matrix theory. Why is this so? In recent years, we have been applying semiclassical and field theoretical concepts to understand the quantumtoclassical crossover in chaotic systems, and the origins of universality. The insights thus gained are now applied to address various applied problems in quantum chaos. 

condensed matter theory: the group has been working on various types of condensed matter systems, notably systems influenced by the presence of static disorder and, more recently, topological condensed matter systems. Examples include disordered metals, superconductors, and topological insulators, various interacting mesoscopic systems ('quantum dots'), and more exotic systems such as random magnetic field systems, graphene, Weyl semimetials, anomalous superconductors, and others. How does the presence of static disorder affect the long range properties of electronic systems? And how will this change if interactions are present? What can be said about quantum interference phenomena and localization properties of condensed matter systems carrying topological indices, or systems with linear (relativistic) spectra? We are working on these and related questions. 

nonequilibrium systems: a third research focus of our group are out of equilibrium phenomena, both classical and quantum. For example, we have studied how dynamically driven quantum systems (the LandauZener problem being the most elementary paradigm) evolve in the presence of interactions. We are also apply methodology of quantum theory (such as the classical limits of Keldysh nonequilibrium techniques) to the study of large fluctuations in biological systems. Concrete problems include the analysis of chaos or statistical fluctuations in small ecological networks. 
A list of recent publications can be found here.