My research interests are focused on differential geometry and topology, mathematical physics, and symplectic geometry. I specialize in J-holomorphic curves, which are a powerful tool for understanding the structure of symplectic manifolds and are also important in string theory as they represent the worldsheets traced out over time by strings. To study J-holomorphic curves, I use degenerations where they limit to piecewise linear graphs, which are reminiscent of interacting particle trajectories and are known as tropical curves. To handle this mathematics, I have developed a technical tool called an exploded manifold, related to something called a log scheme in algebraic geometry. Exploded manifolds allow me to apply differential geometric techniques in degenerate and singular situations.