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,...,v_k and V₁,...,V_k, 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 V_i must also hold between the Dehn twists in the v_i. Time allowing, we will give some corollaries, such as embeddings of certain interesting groups into auto-equivalence groups of Fukaya categories.