Wenyuan Li, a mathematician at the University of Southern California, presents a research seminar talk given through the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. He examines contact homeomorphisms, the limit points of compactly supported contactomorphism groups under the C0-topology, building on a result of Dimitroglou Rizell and Sullivan showing that smooth images of closed Legendrians under such maps remain Legendrian. Li extends the question to coisotropic submanifolds and to whether Maslov data and Floer-theoretic invariants survive these limits. He outlines an approach using microlocal sheaf theory on cosphere bundles with their standard contact structures, joint work with Tomohiro Asano, Yuichi Ike, and Christopher Kuo. The talk assumes graduate-level familiarity with symplectic and contact geometry and works through the sheaf-theoretic machinery used to attack these rigidity questions.