Dr. Stange is especially interested in the relationship between geometry and number theory. She is currently interested in the arithmetic of Kleinian groups, particularly the interplay between algebraic number theory and hyperbolic geometry. Other work focusses 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 cryptography. She has wide-ranging interests, including Apollonian circle packings, elliptic curves, arithmetic dynamics and game theory.

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Number theory, arithmetic geometry, Kleinian groups, elliptic curves, integer sequences, cryptography, arithmetic dynamics, Apollonian circle packings, game theory