The second moment of the size of the 2-Selmer group of elliptic curves

December 9, 2021
This is joint work with Agustin Moreno and Dayung Koh. The restricted three-body problem is invariant under various antisymplectic involutions. These real structures give rise to the notion of symmetric periodic orbits which simultaneously have a closed string interpretation namely as a periodic orbit as well as an open string interpretation as Hamiltonian chords. This makes the bifurcation analysis of symmetric periodic orbits very intriguing since under bifurcations two local Floer homologies are invariant, the periodic one as well as the Lagrangian one. In this talk we explain how methods from symmetric space theory can help to extract efficiently datas from reduced monodromy matrices of periodic orbits helping to analyse the possible bifurcation patterns.