## Nonlinear averaging and parabolic flows

### Matthew Rudd

Sewanee, The University of the South

I will discuss new exponential formulas for the solutions of nonlinear parabolic initial-value problems; for a given problem, the resulting formula is based on the local spatial statistics of the generator of the related nonlinear semigroup. These representations provide new tools for analyzing parabolic flows and their corresponding stationary problems, and their generalizations offer interesting approaches to flows with metric measure space domains and targets.