Pedro Salomão, speaking in the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar, presents joint work with Xijun Hu, Lei Liu, Yuwei Ou, and Zhiwen Qiao on the global dynamics of the spatial isosceles three-body problem. He builds the argument from Embedded Contact Homology, showing that below a critical energy level the flow admits a disk-like global surface of section bounded by the Euler orbit. Estimates on the contact volume of the energy surface and on the rotation number of that orbit, combined with a refinement of Hutchings' mean action theorem, are used to force the existence of infinitely many periodic orbits and to constrain how they wind relative to each other through a twist interval. He also covers the unbounded energy surfaces above the critical level, where twist behavior near infinity yields infinitely many periodic and parabolic trajectories. The talk assumes familiarity with contact and symplectic geometry and targets researchers in dynamical systems.