- Determine how the dimension of the 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);
- Work out the relevant Schubert Calculus to count hyperplane arrangements with fixed intersection lattice that pass through a fixed number of points in the ambient space (with Max Wakefield and Tom Paul);
- Write notes about intersection theory (Schubert calculus, Grassmannians, etc.) aimed at undergraduate and begining graduate students;
- Use secant varieties to study reducible varieties that contain a complete intersection of lines, a project related to liaison theory.