Caleb Springer

Contact Information

Office: Room 602, 25 Gordon St
Department of Mathematics
University College London
London WC1H 0AY

Currently, I am a Heilbronn Research Fellow at University College London. I completed my PhD at Pennsylvania State University in 2021, where my advisor was Professor Kirsten Eisenträger. I enjoy thinking about a wide variety of topics in arithmetic geometry and algebraic number theory, including abelian varieties over finite fields, and problems of decidability and definability.


  1. Abelian varieties over finite fields and their groups of rational points, with Stefano Marseglia. (arXiv preprint.)


  1. Definability and decidability for rings of integers in totally imaginary fields, Bulletin of the London Mathematical Society. Published electronically: 02 October 2023. (arXiv version.)

  2. A topological approach to undefinability in algebraic extensions of ℚ, with Kirsten Eisenträger, Russell Miller and Linda Westrick. Bulletin of Symbolic Logic. Published electronically 29 September 2023. (arXiv version.)

  3. Doubly isogenous genus-2 curves with D4-action, with Vishal Arul, Jeremy Booher, Steven R. Groen, Everett W. Howe, Wanlin Li, Vlad Matei and Rachel Pries. Mathematics of Computation, Volume 93, 2024, Pages 347-381. Published electronically: August 31, 2023. (arXiv version.)

  4. Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽2, 𝔽3, and 𝔽5, with Stefano Marseglia. Proceedings of the American Mathematical Society, Volume 151, Number 2, February 2023, Pages 501–510. (arXiv version.)

  5. The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field. European Journal of Mathematics, Volume 7, Pages 1124–1136 (2021). (arXiv version)

  6. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves, with Edgar Costa, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, and Mckenzie West. Arithmetic Geometry, Number Theory, and Computation, Simons Symposia. (arXiv version)

  7. Undecidability, unit groups and some totally imaginary infinite extensions of ℚ, Proceedings of the American Mathematical Society, Volume 148, Number 11, November 2020, Pages 4705-4715. (arXiv version)

  8. Computing the endomorphism ring of an ordinary abelian surface over a finite field, Journal of Number Theory, Volume 202, September 2019, Pages 430-457. (arXiv version)

Teaching Experience

University College London: The Pennsylvania State University: