Manchester Geometry Seminar - Adrian Dawid
| Dates: | 12 January 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: Adrian Dawid (Cambridge)
Title: Random walks on the Hamiltonian diffeomorphism group
Abstract: On a symplectic manifold M, the group of Hamiltonian diffeomorphisms Ham(M) is a fundamental object of study. When M represents the phase space of a mechanical system, Ham(M) encodes all possible motions. In this talk, we introduce a probabilistic model for Hamiltonian diffeomorphisms. The group Ham(M) is generated by the subset of autonomous Hamiltonian diffeomorphisms, and we construct a natural probability measure on this generating set. This measure arises from a Gaussian measure on the space of smooth functions on the underlying manifold M. After reviewing the basic properties of this construction, we investigate the resulting random walks on the Hamiltonian diffeomorphism group. We conclude with a discussion of several open problems.
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Frank Adams Room 1
Alan Turing Building
Manchester
