The 2019 DOmath program ran from May 20 to July 12, 2019. Here are the five projects, along with the teams' summaries of what they accomplished. The links contain more detailed information, including more technical summaries and final reports where available. Each project's web page now contains a video of students from the team describing their project and experience.
Mysterious unramified zeta functions, led by Professor Jayce R. Getz
Nahm's equations are a system of nonlinear ordinary differential equations that come from mathematical physics, in particular, gauge theory and particle physics. They arise out of the Nahm transform, which allow solutions of Nahm's equations to be transformed into solutions of a much more complicated partial differential equation problem, and vice versa. From purely mathematical perspective, the space of solutions to Nahm's equations is interesting because it has a particularly nice geometry. Since the nonlinearity of the system almost precludes a general solution, we utilized the natural structure that the equations are defined on and exploited symmetries of Nahm's equations to construct and study solutions in special cases. We also performed numerical studies of the equations.