Slava Rychkov, Ecole Normale Superieure
Conformal Field Theories and Bootstrap

Conformal field theories are good friends for both physicists (since they have many applications to critical phenomena, condensed matter, and high energy physics) and mathematicians (they are mathematically well-defined). In two dimensions, conformal field theories have been studied to near-exhaustion. In three and four dimensions, much less is known, and the field is wide open. I will discuss the 'bootstrap' system of equations which, in a sense, defines conformal field theories, and recent results following from the numerical exploration of this system. I will argue that many more results lie ahead ready to be discovered by the same methods. The whole story is crying out for an analytical understanding.