Embedding Obstructions for Non-Toric Rational Surfaces from Newton-Okounkov Bodies

ECH capacities have found many applications to symplectic embedding problems, most of which in the toric setting. I will discuss a new application of ECH to studying optimal embeddings for non-toric rational surfaces. The key convex geometric objects in our story are Newton-Okounkov bodies, which supply embeddings by work of Kaveh and also compute ECH capacities by joint recent work with Julian Chaidez.