Manchester Geometry Seminar - Rubén Izquierdo López
| Dates: | 30 March 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Rubén Izquierdo López (ICMAT, Madrid)
Title: The geometry of variational problems: An introduction to multisymplectic geometry
Abstract: It is well known that autonomous classical mechanics can be described using symplectic geometry. By introducing a symplectic structure on an even-dimensional manifold (usually the cotangent bundle of a configuration manifold), one may obtain the equations of motion, compute Noether symmetries, or reduce the system in the presence of symmetries in an intrinsic, coordinate-independent manner. It is then natural to ask whether one can perform the same analysis for general variational problems, which are usually formulated in terms of sections of a fiber bundle. The ubiquitous objects in this case are the Poincaré–Cartan form and its exterior differential, which allow one to generalise many of the structures and procedures known from mechanics to field theories. In this talk, I will present this geometric framework, explain which notions are readily generalized and which require further analysis. Finally, I will discuss some open questions.
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Frank Adams Room 1
Alan Turing Building
Manchester
