McDuff and Schlenk recently determined exactly when a four-dimensional symplectic ellipsoid symplectically embeds into a symplectic ball. Similarly, Frenkel and Müller recently determined exactly when a symplectic ellipsoid symplectically embeds into a symplectic cube. Symplectic embeddings of more complicated sets, however, remain mostly unexplored. We study when a symplectic ellipsoid symplectically embeds into a polydisc . We prove that there exists a constant depending only on (here, is assumed greater than ) such that if is greater than , then the only obstruction to symplectically embedding into is the volume obstruction. We also conjecture exactly when an ellipsoid embeds into a scaling of for , and conjecture about the set of such that the only obstruction to embedding into a scaling of is the volume. Finally, we verify our conjecture for .
"Symplectic embeddings of four-dimensional ellipsoids into polydiscs." Involve 10 (2) 219 - 242, 2017. https://doi.org/10.2140/involve.2017.10.219