Renormalization group flows for nonlinear PDE

I will discuss a probabilistic approach to the Nash embedding theorems along with several applications. The initial motivation for this work were the results of De Lellis and Szekelyhidi linking Nash embedding with the Euler equations. The main idea in my work is to replace ad hoc construction schemes with a principled choice of stochastic flows, in order that one may answer the question "what does a typical embedding look like?". More precisely, we ask how one may construct natural probability measures supported on solutions to nonlinear PDE.

This idea will be illustrated with examples. This program is still some ways away from completely new proofs of these theorems, however it yields many new models and new insights into Nash-Moser and KAM theorems. Most of the effort at this point is in sharpening the fundamental insight through numerics. In particular, there is a stong interplay with interior point methods for semidefinite programming.

Please contact Jianfeng Lu (jianfeng@math.duke.edu) for virtual meeting link