Title: The Two-Dimensional Standing Water Wave Problem: Is There a Simpler Solution?"
Speaker: Savana Ammons(UIUC)
Abstract: In 2005, Iooss, Plotnikov, and Toland solved the two-dimensional standing water wave problem. By doing so, they became the first people to show that two-dimensional standing water waves under the influence of gravity exist. The catch? Their proof was over 100 pages long and relied on the notoriously complicated Nash-Moser theorem. But is there a simpler way to solve the problem? In this talk, we'll propose an alternative solution method that relies on simpler tools like induction, the comparison test, and rigorous numerics. We'll also provide numerical evidence to suggest that such a method could work.
