|Institute of Geometry and Physics at the University of Science and Technology of China
In this talk, we will provide new examples of star-shaped (toric) domains in C^2 that are dynamically convex but not symplectically convex. Our examples are based on two approaches: one is from Chaidez-Edtmair’s criterion via Ruelle invariant and systolic ratio; the other is from the ECH capacities and an analog non-linear version of Banach-Mazur distance in symplectic geometry. In particular, from the second approach, we derive the first family of examples that can be numerically verified (instead of taking a certain limit from the first approach). We will also illustrate that the information given by these two approaches is in general independent of each other. This talk is based on joint work with Dardennes, Gutt, and Ramos.