Jo Nelson received her PhD in 2013 from the University of Wisconsin - Madison under Mohammed Abouzaid. She previously held concurrent appointments, in part as an NSF postdoctoral fellow, at the Institute for Advanced Study (2013-2016), the Simons Center for Geometry and Physics (2014), and Columbia University (2013-2018). Jo studies symplectic and contact topology, a field, which has its origins in the study of classical mechanical systems. Understanding the evolution and distinguishing transformations of these systems necessitated the development of global invariants of symplectic and contact manifolds. Her research primarily concerns providing foundations and applications for contact invariants stemming from nonequivariant and (circle) equivariant constructions of contact homology. Contact homology is built out of closed orbits of Reeb vector fields and counts of solutions to a nonlinear Cauchy-Riemann equation, which interpolates between closed Reeb orbits. Reeb vector fields are Hamiltonian-like vector fields, whose flow lines are solutions to Hamilton's equations of motion, as they conserve energy. Closed Reeb orbits are of particular interest because they can be used to describe local distance minimizing "loops."