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Motivated by SYK model, there have been a lot of activities to understand quantum dynamics in interacting systems via many-body quantum chaos and describe a variety of quantum phases, e.g., heavy Fermi liquids, marginal and non-Fermi liquid, correlated superconductors, etc., through generalizations of the SYK model. I will first discuss some quantum spin glass models related to the SYK model and the characterization of their dynamics through chaos. I will then discuss some lattice and higher-dimensional generalizations of the SYK model to understand higher-dimensional non-Fermi liquids, such as strange metals and other correlated phases. 

The description of a quantum many-body system lacking quasiparticles is a longstanding challenge at the forefront of physics. A solvable example is provided by the Sachdve-Ye-Kitaev (SYK) model, which has attracted much attention due to its intriguing connections to black holes and intertwined questions on non-Fermi liquid metals, thermalization, and many-body quantum chaos. After a brief review of the phenomenology of Fermi (FL) and non-Fermi (NFL) liquids, I will give a pedagogical introduction to the large-N saddle-point method, spectral and thermodynamics properties, and the computation of the out-of-time-ordered correlation and Lyapunov exponent in the SYK model. I will then discuss a few generalizations/extensions of the SYK model with NFL-FL and other dynamical transitions. I will conclude with a discussion of an experimental realization of the SYK model in condensed matter systems. 

We will discuss connections between quantum relative entropy and other distance measures between probability distributions and quantum states. We will discuss the connection to hypothesis testing. If there is time, we will present applications of classical and quantum information theory to problems in combinatorics and computer science.