I am a Research Fellow at St John's College and a member of the number theory group at DPMMS, University of Cambridge.
I am interested in algebraic and arithmetic geometry; more specifically, arithmetic statistics, rational points, special families of curves and abelian varieties, algebraic cycles, and applications of representation theory to number theory and algebraic geometry.
You can send me an email at: jcsl5(at)cam(dot)ac(dot)uk
In reverse chronological order of arXiv submission. Note that preprints might not always include changes made before publication.
Lower bounds on heights of odd degree points on hyperelliptic curves. Preprint, joint with Jack Thorne. [pdf]
Vanishing criteria for Ceresa cycles. Preprint, joint with Ari Shnidman. [arxiv]
100% of odd hyperelliptic Jacobians have no rational points of small height. Preprint, joint with Jack Thorne. [arxiv]
A positive proportion of monic odd-degree hyperelliptic curves of genus g≥4 have no unexpected quadratic points. IMRN. With Ashvin Swaminathan. [arxiv]
Ceresa cycles of bielliptic Picard curves. J. Reine Angew. Math. (Crelle). Joint with Ari Shnidman. [arxiv]
Rational torsion points on abelian surfaces with quaternionic multiplication. Forum Math Sigma. With Ciaran Schembri, Ari Shnidman and John Voight. [journal][arxiv]
The geometry and arithmetic of bielliptic Picard curves. Preprint, joint with Ari Shnidman. [arxiv]
Graded Lie algebras, compactified Jacobians and arithmetic statistics. Journal of the European Mathematical Society. [journal][arxiv] ([video] and [slides] from a talk about this work.)
Arithmetic statistics of Prym surfaces. Mathematische Annalen. [journal][arxiv]
The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3. Algebra & Number Theory. [journal][arxiv]
Teaching
Current: Part III Lie algebras. See the Moodle page for Example Sheets and more information. Here are the lecture notes: [pdf]
Spring 2023: MAT449 Representation theory. Here are the lecture notes: [pdf]
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!
