Katherine E. Stange

I am a number theorist, and, in Dyson's classification, a frog. I like simple-seeming questions that lead to a richness of structure — arithmetic questions with geometric and especially visual access points.

My interests include elliptic curves, Apollonian circle packings, Kleinian groups, algebraic divisibility sequences, Diophantine approximation, continued fractions, quaternion algebras, and quadratic and hermitian forms, with connections to arithmetic dynamics, homogeneous dynamics, expander graphs, hyperbolic geometry, algebraic groups and lattices. I am also interested in cryptography — especially elliptic-curve and isogeny-based — quantum algorithms, and problems that involve experimental, algorithmic, and especially visual mathematics.