I am currently a second year PhD student at ENS Paris under the supervision of Vincent Vargas. There are two main axes in my research work: Gaussian multiplicative chaos (GMC) and Liouville quantum gravity (LQG). GMC is a random measure with density given by exponential of a log-correlated Gaussian field. It has applications in random matrices, random geometry, statistical physics, finance etc. On the other hand, LQG is a physics theory which lies at the interface of quantum field theory and conformal field theory. My goal is to prove rigorously some conjectures in LQG and deduce as a consequence exact results on GMC.
I am in charge of the course "Mathématiques et statistiques pour économistes" for the statistics part at ENS Paris.