Caleb Springer


Contact Information

Email: cks5320@psu.edu
Office: 015 McAllister Building
Department of Mathematics
The Pennsylvania State University
University Park, PA 16802


I am a PhD student at Penn State University and I expect to graduate in Spring 2021. My advisor is Professor Kirsten Eisenträger. I enjoy thinking about a wide variety of topics in arithmetic geometry and algebraic number theory, including the arithmetic of abelian varieties, post‑quantum cryptography, and problems of decidability and definability.


Papers

  1. Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽2, with Stefano Marseglia. (arXiv preprint.)

  2. 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. (arXiv preprint.)

  3. A topological approach to undefinability in algebraic extensions of ℚ, with Kirsten Eisenträger, Russell Miller and Linda Westrick. (arXiv preprint.)

  4. The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field. European Journal of Mathematics. Published online 23 March 2021. (arxiv version)

  5. Restrictions on Weil polynomials of Jacobians of hyperelliptic curves, with Edgar Costa, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, and Mckenzie West. To appear in the Simons Symposia volume for the Simons Collaboration on "Arithmetic Geometry, Number Theory, and Computation".

  6. 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)

  7. 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