Title: Bakry-Emery theory and renormalisation

Abstract: I will discuss an approach to log-Sobolev inequalities that
combines the Bakry-Emery theory with renormalisation and present several
applications. These include log-Sobolev inequalities with polynomial
dependence for critical Ising models on Z^d when d>4 and singular SPDEs
with uniform dependence of the log-Sobolev constant on both the
regularisation and the volume. The talk is based on joint works with
Thierry Bodineau and Benoit Dagallier.