GAMP seminar by Enno Lenzmann (U Basel)

GAMP (Geometric Analysis and Mathematical Physics) Seminar.

Speaker: Enno Lenzmann (U Basel)

Title: On Energy-Critical Half-Wave Maps into the Two-Sphere: Solitons and Lax Pair Structure.

Abstract: The energy-critical half-wave maps equation arises as a classical continuum limit of Calogero-Moser and Haldane-Shastry type spin systems in one space dimension. In this talk, I will discuss some essential features such as the complete classification of traveling solitary waves with finite energy, by using a close connection to minimal surfaces with free and non-free boundary conditions. Furthermore, I will present a recently found Lax pair structure and we explain its potential applications to the dynamics of the half-wave maps equation. Finally, I will mention some open problems.
This talk is based on joint work with P. Gérard (Orsay) and A. Schikorra (Pittsburgh).