Speaker: Prof.Enno Lenzmann ，University of Basel, Switzerland

Inviter: 张翼副研究员

Title: An invitation to the half-wave maps equation

Language: English

Time & Venue: 2024.09.17 15:00-15:50 N818 Zoom meeting: 878 4974 2364 Code: AMSS2024

Abstract: In this mini-course, I will present a detailed introduction to the current state of affairs for the so-called half-wave maps equation (HWM). This is a quasi-linear Hamiltonian geometric PDE for maps valued in the standard unit sphere S^2. As recently discovered in joint work with P. Gérard (Paris-Orsay), it turns out that (HWM) is completely integrable with a Lax pair structure acting on Hardy spaces. After a brief review of the physical and mathematical motivations for (HWM), based on so-called spin Calogero-Moser systems, I will discuss 1) multi-solitons, 2) explicit flow formulae, 3) its Lax pair structure with Toeplitz and Hankel operators, as well as 4) global well-posedness and soliton resolution for rational initial data. Most of the mini-course material is based on joint works with P.Gérard. If time permits, I will finally provide a brief comparison to a related scalar-valued PDE, the so-called Calogero-Moser derivative NLS (CM-DNLS).