Gaussian free field and Liouville quantum gravity

Understand

Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in which the problem was reduced to the study of certain "random surfaces".

• He further made the tantalising suggestion that this theory could be explicitly solved.
• Recent breakthroughs from the last fifteen years have not only given a concrete mathematical basis for this theory but also verified some of its most striking predictions, as well as Polyakov's original vision.
• This theory, now known in the mathematics literature either as Liouville quantum gravity or Liouville conformal field theory, is based on a remarkable combination of ideas coming from different fields, above all probability and geometry.