1) Investigation of statistical and dynamical manifestations of quantum chaos in many-body systems, using tools such as Random Matrix Theory (RMT) and Krylov space methods. A particular focus on non-Hermitian, open quantum systems, and their gravitational dual, with an emphasis on understanding their chaotic dynamics—known as dissipative quantum chaos.
2) Bridging RMT with free probability theory—to gain new perspectives on physical phenomena such as thermalization, ergodicity, localization, and the mechanisms underlying black hole dynamics.
3) Developing simplified models and quantum circuits and investigating their properties, such as quantum magic, etc., with a focus on implementing their real-time dynamics on near-term quantum devices.