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:十大正规网赌游戏
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。