Nicki Magill, a mathematician at UC Berkeley, presents this research talk from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar on convex toric domains, four-dimensional subsets defined as preimages of bounded convex regions under the moment map. Magill examines how geometric features of these regions, including the curviness of the boundary and its affine perimeter, affect symplectic packing problems. The core tool is embedded contact homology capacities, which obey a Weyl law tied to volume; Magill shows their subleading asymptotics detect affine perimeter instead, and traces how this feeds into new results on symplectic embedding problems. The work is joint with Dan Cristofaro-Gardiner and Dusa McDuff. The talk is pitched at specialists in symplectic and contact geometry, building directly on known capacity results rather than introducing the field from scratch, and runs through the asymptotic arguments and their embedding applications in detail.