The seminar is devoted to a wide range of studies, the core of which is the relationship between the physics of gravitational phenomena, quantum chaos and quantum information, in particular, studies that have appeared at the junction of these sciences in recent years.

The seminar is expected to analyze by graduate students and students (specializing in theoretical and mathematical physics) both articles that have already become classics and very recent ones devoted to the specified range of phenomena.

As is known, gravity (as well as string theory) have always been considered the most "non-applied" sciences, while quantum theory (fields) and its methods, mainly perturbation theory and Green's function methods, have widely penetrated into "applied" physics, for example, condensed matter physics.

Meanwhile, in recent years, various approaches to the non-perturbative description of quantum phenomena (as well as new phenomena that are important to describe) have been discovered, organically combining gravity, quantum information and research in the field of chaos. The range of phenomena to be considered is quite wide. It includes entanglement and quantum complexity (as well as their generalizations), quantum chaos and gravity, nonequilibrium systems and properties of quantum matter (including exotic matter).

On the other hand, it is also expected to understand how the microscopic theory of black holes and string theory determine the properties of these phenomena and how they are directly related to them.

Program
(the order of presentation of topics may vary depending on the audience)

1. Entanglement entropy in quantum field theory and gravity. Entanglement entropy in two-dimensional conformal field theory and its generalizations (reflected entanglement, negativity of entanglement), modular Hamiltonian and its properties. These quantities in nonequilibrium conformal field theory and their connection with the physics of gravitational phenomena.

2.1. Classical and quantum chaos, connection with the physics of black holes. The phenomenon of quantum scrambling in gravity and quantum systems. Quantum complexity theory and complexity in quantum systems and gravity, fundamental constraints on computability following from black hole physics.

2.2. Quantum information theory and gravity — quantum error-correcting codes in gravity and quantum field theory, coding protocols, connection with complexity in physics.

3. Black hole/cosmology models in the context of 1, 2.1, 2.2, and their connection with low-dimensional quantum theories (example: connection between two-dimensional gravity and SYK-type theories, Fermi gas theory and Lin-Lunin-Maldacena solutions, connection with random matrix theories).

Seminar organizer
Ageev Dmitry Sergeevich

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center