Title: Long time dynamics of water waves
Abstract: In this talk I will examine recent breakthrough results in understanding the long-time dynamics of space-periodic water waves, focusing on
1) KAM theory: bifurcation of Cantor-like families of quasi-periodic solutions, both standing and traveling,
2) Birkhoff normal form theory: long-time well-posedness,
3) Modulational instability of Stokes waves: unstable Bloch-Floquet waves near periodic Stokes waves.