Michael Usher

Michael Usher is Professor and Department Head in the Mathematics Department at the University of Georgia, affiliated with the topology and geometry research groups.

His research centers on symplectic topology, investigating global properties of spaces with geometric structures fundamental to classical mechanics. Key focus areas include symplectic four-manifolds, Lefschetz fibrations, Hamiltonian dynamics, symplectic diffeomorphisms, symplectic embeddings, and foundational aspects of filtered Floer and Morse homology. He has developed computational tools for four-dimensional symplectic embedding problems and maintains extensive lecture notes covering advanced topics in symplectic geometry and topology.

Usher teaches graduate courses including Topology of Manifolds (MATH 8210) and has authored comprehensive lecture materials on symplectic geometry, pseudoholomorphic curves, elliptic PDEs on manifolds, and vector bundles. His pedagogical resources—totaling over 400 pages across multiple courses—emphasize accessibility for students with foundational knowledge in smooth manifolds and differential forms, featuring combined notes from Spring 2019 and Spring 2024 introductory symplectic courses.