Current Projects

• Determine how the dimension and degree of the (embedded) moduli space of line arrangements in the projective plane that have a fixed intersection lattice depends on the combinatorics of the lattice (with Max Wakefield);
• Use secant varieties to study reducible varieties that contain a complete intersection of lines, a project related to liaison theory.
• Study the invariant theory and Grassmann-Cayley expressions that determine when 10 points lie on a cubic curve (with David Wehlau).
• Investigate ways in which compressed sensing and the singular value decomposition arise in algebraic problems.
• Understand why reinforcement learning makes systems like AlphaZero so effective at playing certain games. Extend these ideas to operational settings in Navy relevant domains.