报告题目：Desingularizing singular symplectic structures
报 告 人：Eva Miranda
所在单位：Polytechnic University of Catalonia
报告时间：2024年10月18日 20:00-22:00
报告地点：Zoom Id: 904 645 6677，Password: 2024
会议链接：
https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
报告摘要: The exploration of symplectic structures on manifolds with boundaries has naturally led to the identification of a “simple” class of Poisson manifolds. These manifolds are symplectic away from a critical hypersurface, but degenerate along this hypersurface. In the literature, they are referred to as b-symplectic or log-symplectic manifolds. They arise in the context of the space of geodesics of the Lorenz plane and serve as a natural phase space for problems in celestial mechanics such as the restricted 3-body problem. Geometrically, these manifolds can be described as open symplectic manifolds endowed with a cosymplectic structure on the open ends.
The technique of "deblogging" or desingularization associates a family of symplectic structures to singular symplectic structures with even exponent (known as b^{2k}-symplectic structures), and a family of folded symplectic structures for odd exponent (b^{2k+1}-symplectic structures). This method has good convergence properties and generalizes to its odd-dimensional counterpart, contact geometry. In this way, the desingularization technique puts under the same umbrella various geometries, such as symplectic, folded-symplectic, contact, and Poisson geometry.
The desingularization kit has a broad range of applications, such as the construction of action-angle coordinates for integrable systems, KAM theory, quantization, and counting periodic orbits.
报告人简介：Eva Miranda is Chair in Geometry and Topology in the Department of Mathematics at the Polytechnic University of Catalonia, and a member of CRM. She has been a visiting professor at the Paris Observatory, MIT, the University of Toulouse, and the University of Paris 7, and she was an honorary professor at CSIC and an Affiliate Researcher at the Paris Observatory. Miranda is the director of the Geometry and Dynamical Systems Laboratory at UPC and the leader of the Geometry of Manifolds and Applications research group at UPC.
Miranda has been awarded two consecutive ICREA Academia prizes (in 2016 and 2021), a Chair of Excellence from the Paris Mathematical Sciences Foundation in 2017-2018, a Bessel Award from the Humboldt Foundation in 2022, and the François Deruyts Prize in 2022. She was invited speaker at the 8ECM. She was named Hardy Lecturer 2023 by the London Mathematical Society and Nachdiplom Lecturer 2025 by ETHZ. In 2024, she was appointed Gauss Professor by the University of Göttingen.
