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学术报告1:Maciej Dunajski — Integrable systems

时间:2024-01-02 作者: 点击数:

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

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。

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