  In these notes we describe heuristics to predict computational-to-statistical
gaps in certain statistical problems. These are regimes in which the underlying
statistical problem is information-theoretically possible although no efficient
algorithm exists, rendering the problem essentially unsolvable for large
instances. The methods we describe here are based on mature, albeit
non-rigorous, tools from statistical physics.
  These notes are based on a lecture series given by the authors at the Courant
Institute of Mathematical Sciences in New York City, on May 16th, 2017.
