About the Lectureship:
The LMS Hardy Lectureship is named after G.H. Hardy, former President of the Society and De Morgan Medallist. Originally awarded to a distinguished overseas mathematician in odd-numbered years.
The LMS Hardy Lecturer visits the UK for a period of about two weeks, and gives the Hardy Lecture at a Society meeting, normally held in London in July. The LMS Hardy Lecturer also gives at least six other lectures, on different topics, at other venues in the UK; the schedule is decided by the LMS Society, Lectures and Meetings Committee in consultation with the LMS Hardy Lecturer, and is designed to allow as many UK mathematicians as possible to benefit from the LMS Hardy Lecturer's presence in the UK.
Abstract:
Desingularizing singular symplectic structures
The investigation of symplectic structures on manifolds with boundary led naturally to a class of Poisson manifolds which are symplectic manifolds away from a (critical) hypersurface but degenerate along this hypersurface. In the literature, these manifolds are called b-symplectic (or log-symplectic) manifolds. They also show up in the space of geodesics of the Lorentz plane and furnish a natural phase space for regularized problems in celestial mechanics such as the restricted 3-body problem. The geometry of these manifolds can be described as open symplectic manifolds equipped with a cosymplectic structure on the open ends. The desingularization technique or “deblogging” associates a family of symplectic structures to singular symplectic structures with even exponent (the so-called $b^{b2k}$-symplectic structures) and a family of folded symplectic structures for odd exponent ($b^{b2k+1}$-symplectic structures) and has good convergence properties.
This procedure generalizes to its odd-dimensional counterpart and puts in the same picture different geometries: symplectic, folded-symplectic, contact and Poisson geometry. The applications of this “desingularization kit” include the construction of action-angle coordinates for integrable systems, the study of their perturbation (KAM theory) and the existence of periodic orbits.
Bio:
Eva Miranda is a Full Professor at Universitat Politècnica de Catalunya, specializing in Differential Geometry, Mathematical Physics, and Dynamical Systems. She has been honored with several prestigious awards, including two ICREA Academia Prizes in 2016 and 2021, a 2017 Chaire d'Excellence of the FSMP in Paris, a Bessel Prize in 2022, and the François Deruyts Prize in 2022.
Registration:
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