We look at the following chain of symplectic embedding problems in dimension four.
E(1,a)→Z4(A), E(1,a)→C4(A), E(1,a)→P(A,ba)(b ∈ ℕ≥2), E(1,a)→T4(A).
Here E(1,a) is a symplectic ellipsoid, Z4(A) is the symplectic cylinder D2(A)×R2, C4(A)=D2(A)×D2(A) is the cube and P(A,bA)=D2(A)×D2(bA) the polydisc, and T4(A)=T2(A)×T2(A), where T2(A) is the 2-torus of area A. In each problem we ask for the smallest A for which E(1,a) symplectically embeds. The answer is very different in each case: total rigidity, total flexibility with a hidden rigidity, and a two-fold subtle transition between them.
The talk is based on works by Cristofaro-Gardiner, Frenkel, Latschev, McDuff, Muller, and myself.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
