LMS Hardy Lectureship 2023: Professor Eva Miranda (UPC, Barcelona) - Oxford

Room L4, Mathematical Institute, University of Oxford, Oxford
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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.


Singular Hamiltonian and Reeb Dynamics: First steps

Floer theory, which mimics an infinite dimensional Morse approach to the study of critical points of smooth functions, appeared as an attempt to prove Arnold conjecture. The theory is more or less well understood in some compact cases. Non-compact symplectic manifolds can sometimes be compactified as singular symplectic manifolds where the symplectic form "blows up" along a hypersurface in a controlled way (b^m-symplectic manifolds). In natural examples in Celestial mechanics such as the 3-body problem, these compactifications are given by regularization transformations à la Moser/Mc Gehee etc.  I will use the theory of b^m-symplectic/b^m-contact manifolds (introduced by Scott, Guillemin-Miranda Weitsman, and Miranda-Oms) as a guinea pig to propose ways to extend the study of Hamiltonian/Reeb Dynamics to singular symplectic/contact manifolds. This, in particular, yields new results for non-compact symplectic manifolds and for special (but, yet, meaningful) classes of Poisson manifolds.  Inspiration comes from several results extending the Weinstein conjecture to the context of b^m-contact manifolds and its connection to the study of escape orbits in Celestial mechanics and Fluid Dynamics. Those examples motivate a model for (singular) Floer homology.  I'll describe the motivating examples/results and some ideas to attack the general questions.


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.


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