中国科学院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
偏微分方程研讨班
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （1）
时 间：2024.9.16 15：00-15：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 
. 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).
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报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （2）
时 间：2024.9.16 16：00-16：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （3）
时 间：2024.9.17 15：00-15：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （4）
时 间：2024.9.17 16：00-16：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （5）
时 间：2024.9.19 15：00-15：50
地 点：N820 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （6）
时 间：2024.9.19 16：00-16：50
地 点：N820 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （7）
时 间：2024.9.20 15：00-15：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
报告人：Prof.Enno Lenzmann
(University of Basel, Switzerland)
题 目： An invitation to the half-wave maps equation （8）
时 间：2024.9.20 16：00-16：50
地 点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024
摘 要：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 . 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).
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