Jonathan Love
I am a postdoctoral researcher studying computational number theory and arithmetic geometry at Leiden University. I received a Ph.D. in June 2021 from Stanford University, where I was supervised by Akshay Venkatesh, Dan Boneh, and Ravi Vakil. From 2021-2024 I was a CRM-ISM postdoctoral researcher at McGill University.| Email: | j.r.love [at] math.leidenuniv.nl |
My CV
Research
Publications
1. Rational configuration problems and a family of curves: DOI, arXivJournal of Number Theory, Vol. 269 (2025) pp. 370-396.
2. On elements of prescribed norm in maximal orders of a quaternion algebra: DOI, arXiv
Joint with Eyal Goren. Canadian Journal of Mathematics, Published online (2024), 29 pgs.
3. Torsion phenomena for zero-cycles on a product of curves over a number field: DOI, arXiv
Joint with Evangelia Gazaki. Research in Number Theory, Vol. 10, No. 35 (2024), 19 pgs.
4. Root Numbers of a Family of Elliptic Curves and Two Applications: DOI, arXiv
Indagationes Mathematicae, Vol. 35, Issue 3 (2024) pp. 555-569.
5. Rational Equivalences on Products of Elliptic Curves in a Family: DOI, arXiv
Journal de Théorie des Nombres de Bordeaux, Vol. 32, No. 2 (2020) pp. 923-938.
6. Supersingular Curves With Small Non-integer Endomorphisms: DOI, arXiv, ANTS presentation
Joint with Dan Boneh. Proceedings of the Fourteenth Algorithmic Number Theory Symposium, ed. Steven D. Galbraith. The Open Book Series, Vol. 4, No. 1 (2020) pp. 7-22. Winner of the Selfridge Prize for best paper at ANTS-XIV.
Preprints
7. Hypersurfaces passing through the Galois orbit of a point: arXivJoint with Shamil Asgarli and Chi Hoi Yip. 27 pgs.
8. On ℓ-torsion in degree ℓ superelliptic Jacobians over Fq: arXiv
Joint with Wanlin Li and Eric Stubley. 35 pgs.
9. Supersingular elliptic curves, quaternion algebras and applications to cryptography: arXiv
Joint with Eyal Goren. 62 pgs.
10. Local and local-to-global principles for zero-cycles on geometrically Kummer K3 surfaces: arXiv
Joint with Evangelia Gazaki. 27 pgs.
11. Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's Conjecture for zero-cycles: arXiv
Joint with Evangelia Gazaki. 27 pgs.
12. An Arithmetic Variant of Raynaud's Theorem: arXiv
Joint with Libby Taylor. 16 pgs.
Theses
Isogeny Graphs, Zero-cycles, and Modular Forms: Computations over Algebraic Curves and Surfaces (2021): Stanford LibrariesThesis, PhD in Mathematics at Stanford University. Supervised by Akshay Venkatesh, Dan Boneh, and Ravi Vakil.
Field Extensions Generated by Kernels of Isogenies (2016): U of T Libraries
Thesis, Master of Science at University of Toronto. Supervised by Jacob Tsimerman.