Jun Zhang of the Institute of Geometry and Physics at the University of Science and Technology of China presents a research seminar talk in the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series. He opens with star-shaped domains, also called Liouville domains, the building blocks of modern symplectic geometry in Euclidean space, and reviews known subclasses such as dynamically convex domains, geometrically convex domains, and toric domains, along with the relationships linking them. The talk then moves to new territory: extending these notions to fiberwise star-shaped domains inside the cotangent bundles of tori. Zhang introduces analogous subclasses in this setting and works through large-scale geometric properties and embedding problems that mirror the classical Euclidean questions. The material is joint work with Antong Zhu. This is a specialist research talk aimed at symplectic geometers, dense with definitions and open problems rather than introductory exposition, running about sixty minutes.