abstract: We consider contact manifolds arising as the concave boundary of a symplectic plumbing of disk bundles over symplectic surfaces. Our goal is to investigate properties of the contact structures, such as overtwistedness, tightness, fillability, and algebraic torsion measurements. To initiate these investigations and provide a test case for holomorphic curve computations, we consider concave linear plumbings, whose boundaries are contact lens spaces. We will discuss our preliminary results, and more general hopes and goals. This talk is based on joint work in progress with Aleksandra Marinkovic, Jo Nelson, Ana Rechtman, Shira Tanny, and Luya Wang.