Abstract: Wave Turbulence and Pattern Descriptions

 

1. I will explain to you the reasons that the statistical initial value problem for weakly nonlinear waves has a natural closure of its moment/cumulant hierarchy and outline a host of unresolved and open challenges. 

2. I will explain why many pattern forming systems (fingerprints, clous streets, flower stems) have natural descriptions using macroscopic or averaged coordinates and show how machine learning techniques can identify such coordinate systems. We will also discuss open challenges.