报告时间：

Lecture 1-3：2023年1月8日-1月10日，17：00-18：00

Lecture 4-6：2023年1月15日-1月17日，17：00-18：00

报告地点：Zoom ID：913 2415 4629 Passcode: 052302

报告人：Maciej Dunajski教授

工作单位：剑桥大学

举办单位：数学学院

报告简介：

Integrable systems are nonlinear differential equations which ‘in principle’ can be solved analytically. This means that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare - most nonlinear differential equations admit chaotic behaviour and no explicit solutions can be written down. Integrable systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics. This mini-course will provide an introduction to the subject with the emphasis on the twistor and geometric approach.

Lecture 1. Integrability of ODEs: The first integrals, and Arnold-Liouville Theorem.

Lecture 2, 3. Soliton equations, inverse scattering, Hamiltonian formalism. KdV solitons and Sin-Gordon Kinks.Bogomolny argument.Lecture 4, 5, 6. Self-duality and integrability: Solitonic equations from self-dual Yang—Mills, anddispersionless equations from self-dual conformal structures. Hierarchies.

报告人简介：

MaciejDunajski，英国剑桥大学数学物理教授，博士毕业于英国牛津大学，是2020年诺贝尔物理学奖得主Penrose团队的重要成员。该团队一直关注于统一描述相对论和量子力学的Twistor理论，近年来，深入研究了Twistor理论与无色散可积系统之间的重要联系。2023年Dunajski教授获得了剑桥大学霍金天体物理研究所杰出贡献奖。