Department of Mathematics, UCI

I will begin my talk with a brief overview of WWT during which I aim to give an intuitive picture of the phenomenon using the example of surface water waves. This example will be revisited throughout the talk. Next I will try to give a welcoming (although selective) introduction to the calculations of WWT. Equipped with the results of these calculations, I will discuss the relationship between WWT, power-law spectra (both Kolmogorov-Zakharov and MMT) and intermittency. The challengers to WWT are highly nonlinear events, breakdown and the alternative symmetries of the governing equation. I will make some remarks which point out the interconnectedness of these phenomena and, simultaneously, the goals of my research interests.