In this talk, I will a give a survey of recent results about the mass-critical nonlinear half-wave equation on the line. Furthermore, I will discuss work in progress on the energy-critical half-wave maps equation, which posesses some intriguing connections to completely integrabe spin chains and the theory of minimal surfaces
De Patrick Gerard
De Hatem Zaag
De Thomas Kappeler
De Michal Kowalczyk
De Cécile Huneau
De Mihalis Dafermos
De Andrea Nahmod
De Benjamin Schlein
De Chris Sogge
De Alexandru Ionescu
De Vlad Vicol
De Thomas Alazard
De Robert Jerrard
De Camillo de Lellis
De Albert Schwarz
De Chao Li
De Albert Schwarz
De Albert Schwarz
De Stephen Coombes , Peter Liddle
De Victor Kleptsyn
De François-Xavier Vialard
