*note location change*

Jadwin Hall 4th floor PGI Open Space

I will give an overview of a perspective on Polchinski's continuous formulation of the renormalization group, developed over the last few years with T. Bodineau and B. Dagallier, as well as some applications to functional inequalities and sample path regularity of Euclidean field theories.

Time permitting, I will also discuss connections to other recent and less recent developments such as stochastic localization (Eldan and others), its optimality from a transport perspective (Foellmer) and gradient flow perspective (Cotler-Rezchikov), its variational representation (Boue-Dupuis and Barashkov-Gubinelli), and its application to the construction of transport maps (Kim-Milman and Shenfeld).