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Junior Dynamics Seminar – Fraser Sanders (University of Manchester)

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The Junior Dynamics Seminar will feature Fraser Sanders from the University of Manchester discussing infinite-dimensional contact geometry and conservative contact systems. The seminar aims to explore the generalisation of Hamiltonian mechanics in the context of contact geometry and its applications in thermodynamics.

Infinite-dimensional contact geometry and conservative contact systems Speaker: Fraser Sanders (University of Manchester) Abstract : In finite dimensions, contact geometry is well-studied as an odd-dimensional counterpart to symplectic geometry. It is also a natural setting in which to generalise Hamiltonian mechanics of systems, taking into account a notion of dissipation or diffusion. For example, the simplest example of a contact-Hamiltonian system is the damped harmonic oscillator (the dissipative counterpart to the simple harmonic oscillator). Due to the diffusive properties of the contact-Hamilton equations, it is also a natural setting in which to study thermodynamics (cf. Grmela, Bravetti, and many others). In fact, the 1st law of thermodynamics, $dU = T dS$ can be considered as defining a contact form on $\mathbb{R}^3$. The goal during the seminar is to show that contact geometry can be meaningfully defined in infinite-dimensional manifolds, and to give some elementary examples of infinite-dimensional contact Hamiltonian systems. Time permitting, I will also discuss some subset of: Interesting differences between finite- and infinite-dimensional contact geometry, Infinite-dimensional counterparts of Hopf fibrations, And how to define a large class of conservative contact systems, and some examples of this concept.

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Junior Dynamics Seminar – Fraser Sanders (University of Manchester) takes place on Thursday, 19 November 2026 at 16:00.

Junior Dynamics Seminar – Fraser Sanders (University of Manchester) is held at Huxley Building, South Kensington Campus in London (642, Huxley Building, SW7 2AZ).

Entry to Junior Dynamics Seminar – Fraser Sanders (University of Manchester) is free.

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