Baptiste Cerclé

My research is mostly focused on the mathematical understanding of a family two-dimensional conformal field theories, called Toda Conformal Field Theories, that generalize Liouville quantum gravity. This is achieved thanks to a wide range of tools ranging from probability theory to vertex operator algebras,  representation theory and conformal geometry.

I particularly enjoy interplays between probability theory, mathematical physics and other areas of mathematics, especially when it involves beautiful symmetries. In this perspective two-dimensional conformal field theory provides a rich playground where all these elements are gathered.

Here is a (non-exhaustive) list of topics that I had the chance to work with so far:

• probability theory, and more specifically Gaussian Free Fields, Gaussian Multiplicative Chaos and diffusion processes;

• vertex operator algebras and more precisely W-algebras and their representation theory;

• conformal geometry in dimension two or higher;

• And of course mathematical physics and more precisely conformal field theory, which is the scene where all these protagonists appear!