Manchester Geometry Seminar - Fraser Sanders
| Dates: | 20 October 2025 |
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| Times: | 20:00 - 21:00 |
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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: Fraser Sanders (Manchester)
Title: Contact Geometry in Infinite Dimensions
Abstract: Symplectic geometry has for centuries been used to model physical systems with conserved quantities, while its odd-dimensional counterpart, contact geometry, has been used to model systems with dissipation, notably thermodynamical systems. Symplectic geometry has also been used in infinite dimensions to model ideal fluids Ratiu, Arnold, and others, among other infinite-dimensional systems. So far, no work has been done on generalising contact geometry to infinite dimensions in the same way. I aim to show that there is a very natural definition of contact geometry that readily generalises into infinite dimensions. I will then describe examples of infinite-dimensional contact manifolds (with both Banach and Fréchet topologies), as well as contact-Hamiltonian systems (and their flows) on these manifolds. I will also demonstrate results that parallel properties of finite-dimensional contact forms.
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Frank Adams Room 1
Alan Turing Building
Manchester
