The holographic principle is the idea that a theory of quantum gravity has an alternative description in terms of a non-gravitational theory in a smaller number of dimensions. This principle has been responsible for many recent advances in high energy and condensed matter physics. I will give a basic introduction to holography, and explain how it is related to the Sachdev-Ye-Kitaev models of interacting fermions, and to the study of quantum chaos. I will also describe how the quantum chaotic behavior of holographic theories is intimately connected to their thermal transport properties.

 

The four lectures will cover: Introducation to holography and the black hole thermodynamics, Schwarzian action from AdS2, the Lyapunov exponent from black hole and D~v^2/T from holographic computation.