Markov Staircases

In this talk, we will discuss new infinite symplectic staircases. Much recent progress has been made in the study of infinite symplectic staircases arising from embedding problems of standard ellipsoids into various symplectic four-manifolds. We study new embedding problems, where the domains are "ellipsoid-like" neighbourhoods of Lagrangian pinwheels instead of standard ellipsoids. Using almost toric fibrations, we show that every Lagrangian pinwheel in the complex projective plane (and thus every Markov number) has an infinite symplectic staircase. This is joint work with Jonny Evans, Johannes Hauber and Felix Schlenk.