Lagrangians in integrable systems: a variational principle for symmetries

Speaker: Dr Mats Vermeeren (Loughborough University)

https://www.lboro.ac.uk/departments/maths/staff/mats-vermeeren/

Title: Lagrangians in integrable systems: a variational principle for symmetries

Abstract: Noether’s theorem relates symmetries of a Lagrangian system to conservation laws. This is great, but it treats the Lagrangian system and its symmetries as entirely different entities. Recent developments in integrable systems have shown that a Lagrangian system can be captured together with all its symmetries in a single variational principle. I will give some background on integrable systems and explain this variational principle, with the help of some examples. The talk will be mathematical, but with examples borrowed from physics, so I hope to convey that these ideas are of physical relevance.