Expertise

Number Theory, Arithmetic Geometry, Algebraic Geometry

Research

I am a number theorist with interests in arithmetic and algebraic geometry. I am particularly interested in the study of K3 surfaces, their Picard groups, groups of automorphisms, ample cone, counting the number of rational points or curves with bounded height in orbits, and vector heights and canonical vector heights. Such problems are often related to counting the number of integer points with bounded height on certain hyperbolic hypersurfaces, counting lattice points in hyperbolic geometries, or the study of multi-branch linear trees and their Hausdorff dimensions. I also am interested in classical problems in geometry, particularly those involving constructions with traditional but little studied tools.