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Stange, Katherine E Associate Professor

Positions

Research Areas research areas

Research

research overview

  • 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.

keywords

  • Number theory, arithmetic geometry, Kleinian groups, elliptic curves, integer sequences, elliptic curve cryptography, lattice-based post-quantum cryptography, Diophantine approximation, arithmetic dynamics, Apollonian circle packings

Publications

selected publications

Teaching

courses taught

  • MATH 2001 - Introduction to Discrete Mathematics
    Primary Instructor - Spring 2018 / Spring 2020
    Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-).
  • MATH 3110 - Introduction to Theory of Numbers
    Primary Instructor - Spring 2019
    Studies the set of integers, focusing on divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes.
  • MATH 6180 - Algebraic Number Theory
    Primary Instructor - Spring 2019
    Introduces number fields and completions, norms, discriminants and differents, finiteness of the ideal class group, Dirichlet's unit theorem, decomposition of prime ideals in extension fields, decomposition and ramification groups. Department enforced prerequisites: MATH 6110 and MATH 6140. Instructor consent required for undergraduates.
  • MATH 8114 - Topics in Number Theory
    Primary Instructor - Spring 2020
    May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Department enforced prerequisite: MATH 6110. Instructor consent required for undergraduates.

Background

International Activities

global connections related to teaching and scholarly work (in recent years)

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