Abstract or Additional Information
The mathematical study of water waves began with the derivation of the basic mathematical equations of fluids by Euler in 1752. Later, water waves
(with a free boundary at the air interface) played a central role in the work of Poisson, Cauchy, Stokes, Levi-Civita and many others. It remains a very active area to the present day.
I will consider classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, we now know that there exist many such waves. They are exact smooth solutions of the Euler equations with the physical boundary conditions. I will exhibit some numerical computations of such waves. Many fundamental problems remain open. For instance, how steep can such a wave be?