Jef Laga
Academic Website
My research focuses on the arithmetic and geometry of curves and abelian varieties. Here is my CV (updated August 2025): [pdf]
Coordinates
- Office: EL.06 in the CMS and Cripps F11c in St John's College.
- Email:
jcsl5(at)cam(dot)ac(dot)uk - Here are my arXiv papers and MathSciNet profile.
Research articles
In reverse chronological order of arXiv submission. Note that preprints might not always include changes made before publication.
- Polarizations, torsors and theta groups.
Preprint. (2510.24678) - Families of curves in Vinberg representations.
Preprint, joint with Beth Romano. (2508.09607, code) - Kummers, spinors and heights.
Preprint, joint with Jack Thorne. (2507.06865, code) - Lower bounds on heights of odd degree points on hyperelliptic curves.
Preprint, joint with Jack Thorne. (2507.08652) - Vanishing criteria for Ceresa cycles.
Compositio Mathematica (to appear). With Ari Shnidman. (2406.03891)
([slides] and [video] by me, and [slides] of a survey talk by A. Beauville) - 100% of odd hyperelliptic Jacobians have no rational points of small height.
Preprint, joint with Jack Thorne. (2405.10224)
([slides]) - A positive proportion of monic odd-degree hyperelliptic curves of genus g≥4 have no unexpected quadratic points.
IMRN. With Ashvin Swaminathan. (2405.09421) - Ceresa cycles of bielliptic Picard curves.
J. Reine Angew. Math. (Crelle). Joint with Ari Shnidman. (2312.12965)
([video] by Ari) - Rational torsion points on abelian surfaces with quaternionic multiplication.
Forum Math Sigma. With Ciaran Schembri, Ari Shnidman and John Voight. (2308.15193) - The geometry and arithmetic of bielliptic Picard curves.
Journal of the London Mathematical Society (to appear). With Ari Shnidman. (2308.15297) - Graded Lie algebras, compactified Jacobians and arithmetic statistics.
Journal of the European Mathematical Society. (2204.02048)
([video] and [slides] from a talk about this work.) - Arithmetic statistics of Prym surfaces.
Mathematische Annalen. (2101.07658) - The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3.
Algebra & Number Theory. (2008.13158)
Teaching
Outreach
In the past, I have given talks to high-school students, undergraduates from non-math backgrounds, olympiad contestants and summer school students on various aspects of number theory, geometry and pure mathematics. I am generally happy to give more such talks, especially those focused on outreach and access; please send me an email if you're interested.Reading groups
- Fall 2022: Princeton Arithmetic Statistics learning seminar
- Michaelmas 2021 (Arakelov intersection theory on Shimura Varieties): [schedule]
- Lent-Easter 2021 (Automorphy lifting theorems): [schedule]
- Michaelmas 2020 (Mazur's torsion paper): [schedule]
- Lent-Easter 2020 (Weil II): following chapter I of this book
- Michaelmas 2019 (Average ranks of elliptic curves): following this paper
Other notes
- A note surveying some ADE classifications and connections between them, accompanying my talks ([video1] and [video2]) in Kazhdan's basic notions seminar: [pdf] (The second talk goes further than the note.)
- A note defining the analytification functor in the rigid setting, together with the example of the Tate curve: [pdf]
- Notes for a talk defining the etale homotopy type of a scheme with some examples: [pdf]
- Statement of the Bloch-Kato conjecture on special values of L-functions: [pdf]
- My Part III essay on Modular forms of weight one: [pdf]
- A simple plane curve over the p-adics with bad reduction but whose Jacobian has good reduction:
Miscellaneous
- Check out the Youtube channel Math-life balance, where Mura Yakerson interviews mathematicians in an interesting and personal way
- Bjorn Poonen has great advice on mathematical writing, speaking and being a PhD student
- I strongly support Frederico Ardila's axioms
- Check out Gender bias 101 for mathematicians