2024

The Analysis Autumn School 2024 is scheduled to take place from September 16, 2024, to September 20, 2024, featuring both on-site and online sessions via Zoom. All lectures will be recorded and made available for later viewing, subject to the lecturers' consent.

Herbert Koch (University of Bonn, Germany)

Title: "The Korteweg-de Vries Hierarchy at Low Regularity"

Abstract: The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in L^2, and hence of the Korteweg-de Vries hierarchy in low regularity.

Enno Lenzmann (University of Basel, Switzerland)

Title: "An Invitation to the Half-Wave Maps Equation"

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).

Scientific Committee: Ping Zhang (Chinese Academy of Sciences)

Organizers: Feimin Huang (Chinese Academy of Sciences), Yi Zhang (Chinese Academy of Sciences)

Schedule and Location:

On-site Location and Dates:  N913, South Building of the AMSS (September 16, 17，20);

N820，South Building of the AMSS (September 19).

Zoom Meeting: ID: 878 4974 2364, Code: AMSS2024

• Professor Koch: Daily lectures from 9:00–9:50 AM and 10:00–10:50 AM Beijing time.

• Professor Lenzmann: Daily lectures from 3:00–3:50 PM and 4:00–4:50 PM Beijing time.

Both on-site and online streaming options will be available for all lectures.