I am a theoretical physicist working at the intersection of quantum gravity, quantum field theory and quantum information theory.

Currently, the focus of my research is the emergence of space-time in holography, the non-perturbative renormalization group, and the generalizations of the entanglement theory.

## MY LATEST RESEARCH

Eigenstate Thermalization Hypothesis in Conformal Field Theories

We investigate the eigenstate thermalization hypothesis (ETH) in d+1 dimensional conformal field theories by studying reduced density matrices in energy eigenstates. We show that if local probes of high energy primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.

Gravitational Positive Energy Theorems from Information Inequalities

We argue that classical, asymptotically AdS spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region of the boundary spacetime we associate a natural notion of a gravitational energy that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual CFT state.