Photograph by Mari Kawakatsu

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

Rational configuration problems and a family of curves: arXiv
Accepted for publication in Journal of Number Theory.

On elements of prescribed norm in maximal orders of a quaternion algebra: arXiv
Joint with Eyal Goren. Accepted for publication in Canadian Journal of Mathematics.

Root Numbers of a Family of Elliptic Curves and Two Applications: DOI, arXiv
Indagationes Mathematicae, Vol. 35, Issue 3 (2024) pp. 555-569.

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)

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.

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

Rational l-torsion points on Jacobians of μ_l-covers (in preparation).
Joint with Wanlin Li and Eric Stubley.

Supersingular elliptic curves, quaternion algebras and applications to cryptography: arXiv
Joint with Eyal Goren.

Local and local-to-global principles for zero-cycles on geometrically Kummer K3 surfaces: arXiv
Joint with Evangelia Gazaki.

Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's Conjecture for zero-cycles: arXiv
Joint with Evangelia Gazaki.

An Arithmetic Variant of Raynaud's Theorem: arXiv
Joint with Libby Taylor.

Theses

Isogeny Graphs, Zero-cycles, and Modular Forms: Computations over Algebraic Curves and Surfaces (2021): Stanford Libraries
Thesis, 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.

Teaching

Past Teaching at McGill:

MATH 346 / 377 (Number Theory / Honours Number Theory)
Math 240 (Discrete Structures) (held online)

Past Teaching at Stanford:

CA* for Math 113 (Linear algebra and matrix theory), Winter 2021 (held online)
TA** for Math 51 (Linear Algebra and Multivariable Calculus), Fall 2020 (held online)
CA for Math 104 (Applied Matrix Theory), Spring 2020 (held online)
TA for Math 62DM (Modern Mathematics: Discrete Methods), Winter 2020
CA for Math 120 (Groups and Rings), Spring 2019
TA for Math 51 (Linear Algebra and Multivariable Calculus), Fall 2018
TA for Math 62DM (Modern Mathematics: Discrete Methods), Winter 2018
CA for Math 120 (Groups and Rings), Fall 2017
TA for Math 53 (Ordinary Differential Equations), Spring 2017
CA for Math 120 (Groups and Rings), Fall 2016

* CA: "Course Assistant," responsible for office hours, grading, writing solutions, administrative tasks

** TA: "Teaching Assistant," responsible for running discussion sections with approximately 20 students (1-4 hours per week)

Past Teaching at University of Toronto:

TA for MAT347 (Groups, Rings, and Fields), 2014-15 and 2015-16
TA for MAT137 (Calculus!), 2013-14
TA for MAT187 (Calculus for Engineering Students), Winter 2013
TA for MAT135 (Calculus), Fall 2012