Renormalization, Stochastic PDEs and Statistical physics

Short- and large-scale limits of stochastic PDEs and interacting particle systems through rigorous renormalization group techniques. KPZ equation. Non-linear sigma model.

Schrödinger-Virasoro algebra and dynamical Schrödinger symmetries. Algebraic and geometric study. Action by reparametrization on equations of mathematical physics. Applications to log-gas dynamics. An application to hard-core bosons.