The equations of free surface hydrodynamics describe the motion of waves, such as those on the surface of the ocean. This is a classical problem that has attracted the interest of mathematicians and engineers over the last two centuries, with early studies going back at least to Cauchy, Poisson and Lagrange. The understanding of the motion of waves in the ocean and the atmosphere is clearly a fundamental endeavor for mathematicians, engineers as well as numerical analysts and computational scientists.

Because of the complex nature of the nonlinear problems involved in this area, theoretical advances on some of the basic mathematical questions (e.g., the local-in-time well-posedness of the water waves equations) have only been made relatively recently, starting in the `70s and progressing with major breakthroughs in the late `90s and early `00s.

A spurt of activity in the last two decades has brought major advances, such as, just to name a few, the discovery of certain classes of singular solutions, the constructions of global-in-time dispersive solutions by Fourier analytical methods, and proofs of long-time stability for spatially periodic solutions via dynamical systems and KAM methods.

Despite all these recent advances, several fundamental questions still remain poorly understood, including the interplay of surface waves with non-trivial geometries, the role of vorticity, the existence of global multi-dimensional periodic motions, and the dynamic formation of singularities. These and other important topics, such as large-amplitude waves (e.g. steady or solitary waves) that cannot be captured using perturbative techniques, or the control of waves, will be among the main themes of the workshop. The aim is to gather the most prominent figures across the field to survey the state of the art and launch new investigations into some of the main open questions, while also stimulating the interaction between theory and applications.

All talk times are listed in Eastern time (GMT-4).