Dr. Stange is especially interested in the relationship between geometry and number theory. She is interested in arithmetic geometry, including elliptic and modular curves, as well as the arithmetic of Kleinian groups, particularly the interplay between algebraic number theory and hyperbolic geometry. Other work focuses on the connections between arithmetic recurrence structures (such as integer sequences defined by a recurrence relation) and geometric objects (such as abelian varieties). She is also active in cryptography, including elliptic curve cryptography and lattice-based post-quantum cryptography. She has wide-ranging interests, including Apollonian circle packings, abelian sandpiles, arithmetic dynamics and game theory.