Aneesur Rahman Prize for Computational Physics (2020): What have we learned from Dynamical Mean Field Theory and what lies ahead?

Dynamical Mean-Field Theory (DMFT) provides an original physical perspective on strongly correlated electron materials, as well as an efficient computational framework to understand and predict their properties. In this talk, I will review the main ideas at the heart of the DMFT construction and physical perspective. Through select examples, I will outline how the efforts of a whole community over almost three decades have managed to develop the theory to such a point that it can successfully be applied to a real material, taking into account its structure and chemical composition. I will also outline how the theory is being extended and generalized in many fruitful directions.