Berlin-Hamburg-Seminar am 11.12.2017
Lei Zhao (Augsburg) Convex embedding for the rotating Kepler problem and the Birkhoff conjecture
In this talk, I shall explain that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surface of the planar rotating Kepler problem into R4 endowed with its standard symplectic structure. A direct consequence is the dynamical convexity of the planar rotating Kepler problem, which had been established by Albers-Fish-Frauenfelder-van Koert by direct computation. I shall also explain its relationship with Birkhoff's conjecture about the existence of a global surface of section in the restricted planar circular three body problem.
This work is a result from a collaboration with Urs Frauenfelder (Augsburg) and Otto van Koert (Seoul).
Ailsa Keating (Cambridge) On symplectic stabilisations and mapping classes
In real dimension two, the symplectic mapping class group of a surface agrees with its 'classical' mapping class group, whose properties are well-understood. To what extend do these generalise to higher dimensions? We consider specific pairs of symplectic manifolds (S,M) where S is a surface, together with collections of Lagrangian spheres in S and in M, say v1,...,vk and V1,...,Vk, that have analogous intersection patterns, in a sense that we will make precise. Our main theorem is that any relation between the Dehn twists in the Vi must also hold between the Dehn twists in the vi. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.