Morgan Weiler, Cornell University: Symplectic geometry is the study of 2-forms on even-dimensional manifolds. Its roots are in Hamiltonian mechanics, but the fact that symplectic forms are all locally standard often suggests a global perspective. In low dimensions, symplectic tools are particularly powerful, reproducing gauge theory by counting "pseudoholomorphic" submanifolds. In this talk, we will discuss two recent results – one classifying symplectic embeddings and the other identifying periodic orbits of vector fields – whose proofs rely on computing 3D gauge-theoretic diffeomorphism invariants using symplectic geometry. Joint work with Magill-McDuff, Magill-Pires, and Nelson will be highlighted. We will also mention some avenues for future work and work in progress.