My current research involves Brill-Noether theory of higher rank vector bundles on surfaces, algebraic hyperbolicity, and nef cones of Hilbert schemes of points on surfaces, interpolation problems for line bundles on surfaces, and derived categories of sheaves.
Publications and preprints:
Algebraic hyperbolicity of subvarieties of homogeneous varieties.
Joint with Andy B. Day. Preprint. (2025) pdf
Higher rank Clifford's theorem on the smooth quadric.
Preprint. (2025) pdf
Nef cones of Hilbert schemes of points on some K3 surfaces.
Joint with Uttaran Dutta and Sean Edwards. Preprint. (2025) pdf
Brill-Noether theory on the projective plane for bundles with many sections.
Joint with Izzet Coskun and Jack Huizenga. Int. Math. Res. Not. IMRN. (2025) pdf
Ample cones of Hilbert schemes of points on hypersurfaces in projective 3-space.
Proc. Amer. Math. Soc. (2024) pdf