Jef Laga's homepage

Jef Laga

Welcome to my webpage! I am a Postdoctoral Research Associate at Princeton University.
Recently, I obtained my PhD at the University of Cambridge under the supervision of Jack Thorne.

I am interested in algebraic and arithmetic geometry, with a focus on arithmetic statistics of algebraic curves and abelian varieties.
In my PhD thesis, I have shown how various results in arithmetic statistics can be unified and reproved using the theory of graded Lie algebras.

You can send me an email at: jl0793(at)princeton(dot)edu

Preprints/Publications

• Graded Lie algebras, compactified Jacobians and arithmetic statistics.
Preprint, based on my PhD thesis. [pdf] [arxiv]

• Arithmetic statistics of Prym surfaces.
To appear in Mathematische Annalen. [journal] [arxiv]

• The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3.
To appear in Algebra & Number Theory. [journal] [arxiv]

Teaching

Fall 2022: MAT104 Calculus II

• 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 in this study group 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: $y^4+y^2=x^3+p^6&space;\quad&space;(p&space;\neq&space;2,3)$
• 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