Publications

Publications

• J. Love, E. Studnia, J. Vonk

  Arithmetic intersections on non-split Cartan modular curves

  Submitted · pdf

• H. Darmon, J. Vonk

  p-adic Green's functions for real quadratic geodesics

  Res. Number Theory 11, No. 1, Paper No. 40, 26 p. (2025) · pdf · journal

• J. Vonk

  Rigid cocycles and singular moduli for real quadratic fields

  “Number theory informed by computation”, IAS/Park City Math. Ser. 29, 249–290, Amer. Math. Soc. (2025) · pdf · book

• J. Balakrishnan, N. Dogra, S. Müller, J. Tuitman, J. Vonk

  Quadratic Chabauty for modular curves

  Compositio Math., Vol. 159, No. 6 (2023), 1111–1152 · pdf · journal

• H. Darmon, A. Pozzi, J. Vonk

  The values of the Dedekind–Rademacher cocycle at real multiplication points

  J. Eur. Math. Soc. (JEMS), Vol. 26, No. 10 (2024), 3987–4032 · pdf · journal

• H. Darmon, J. Vonk

  Real quadratic Borcherds products

  Pure Appl. Math. Q. (Special Issue in honor of Dick Gross), Vol. 18, No. 5 (2022), 1803–1865 · pdf · journal

• J. Vonk

  Overconvergent modular forms and their explicit arithmetic

  Bull. Amer. Math. Soc., Vol. 58, No. 3 (2021), 313–356 · pdf · journal

• H. Darmon, J. Vonk

  Arithmetic intersections of modular geodesics

  J. Number Theory (Prime), Vol. 230 (2022), 89–111 · pdf · journal

• A. Lauder, J. Vonk

  Computing p-adic L-functions of totally real fields

  Math. Comp., Vol. 91, No. 334 (2022), 921–942 · pdf · journal

• H. Darmon, A. Pozzi, J. Vonk

  Diagonal restrictions of p-adic Eisenstein families

  Math. Ann., Vol. 379, No. 1 (2021), 503–548 · pdf · journal

• J. Balakrishnan, A. Best, F. Bianchi, B. Lawrence, N. Triantafillou, S. Müller, J. Vonk

  Two recent p-adic approaches towards the (effective) Mordell conjecture

  “Arithmetic L-Functions and Differential Geometric Methods”, Progress in Math., Vol. 338, 31–74, Birkhäuser · pdf · book

• J. Balakrishnan, N. Dogra, S. Müller, J. Tuitman, J. Vonk

  Explicit Chabauty–Kim for the split Cartan modular curve of level 13

  Ann. of Math. (2), Vol. 189, No. 3 (2019), 885–944 · pdf · journal

• H. Darmon, J. Vonk

  Singular moduli for real quadratic fields: a rigid analytic approach

  Duke Math. J., Vol. 170, No. 1 (2021), 23–93 · pdf · journal

• J. Vonk

  Modular eigenforms at the boundary of weight space

  Res. Number Theory, Vol. 4, No. 2 (2018) · pdf · journal

• J. Vonk

  Crystalline cohomology of towers of curves

  Int. Math. Res. Not. (IMRN), Vol. 2020, No. 21, 7454–7488 · pdf · journal

• J. Vonk

  Computing overconvergent forms for small primes

  LMS J. Comp., Vol. 18, No. 1 (2015), 250–257 · pdf · journal

• R. Möller, J. Vonk

  Normal subgroups of groups acting on trees and automorphism groups of graphs

  J. Group Theory, Vol. 15, No. 6 (2012), 831–850 · pdf · journal

Profiles

My publication profile on external databases.

Google Scholar zbMATH Open ORCID

Expository

Some expository mathematical notes for talks, mini-courses, etc.

• Rational points on modular curves

  ICTS Bangalore, September 2023

  Notes from a lecture series at the ICTS Summer School on rational points on modular curves. The focus of this course was on arithmetic properties of cusps and CM points, and to illustrate the works of Mazur and Gross–Zagier in an examples-based way.

• Torsion points on elliptic curves

  Hay-on-Wye, August 2022

  Notes from a mini-course at the CMI Graduate Summer School on elliptic curves, held at Baskerville Hall. The lectures were on the theme of torsion points on elliptic curves, and centre around two foundational results: the theorem of Mazur on torsion of elliptic curves over Q, and the open image theorem of Serre.

• Rigid cocycles and singular moduli for real quadratic fields

  Park City, Utah, August 2022

  Notes from a mini-course at the PCMI 2022 Graduate Summer School, held in Park City. The theme of the programme was Number Theory Informed by Computation, and these lectures focus on the computation of rigid cocycles, and how experiments played a role in the development of their theory.

• Topics in Number Theory: p-Adic L-functions

  Leiden, Spring 2021

  Notes for part of a master course at Leiden. The aim is to give a friendly introduction to the theory of p-adic measures and Mellin transforms, and how they are used to define the Kubota–Leopoldt p-adic zeta function. The approach borrows from the beautiful treatment by Pierre Colmez.

• Some spectral questions over R and Q_p

  IAS Princeton, Spring 2020

  Expanded notes that grew out of an experimental talk in the Séminaire Shimizu. Its aim was to give an introduction to the subject of p-adic modular forms, and explore experimentally a number of analogies with the spectral theory of the Laplacian on Maass forms suggested by Frank Calegari.

• Overconvergent modular forms and their explicit arithmetic

  Bordeaux, June 2019

  Notes from a mini-course at the Iwasawa 2019 summer school. The lectures were about the basic theory of overconvergent modular forms, and their explicit computation following the algorithm of Lauder. An expanded version of these notes was later published in the Bulletin of the AMS.

• Rigid meromorphic cocycles

  Barcelona, June 2017

  A rough set of notes from a series of lectures on joint work with Henri Darmon, given during the summer of 2017 at UPC Barcelona, as part of a seminar run by Víctor Rotger.

Code

Some code written as part of my mathematical research, also available on GitHub.

• Rigid meromorphic cocycles

  Henri Darmon and I wrote a Magma package to compute spaces of rigid meromorphic cocycles, as introduced in our papers

  1. Singular moduli for real quadratic fields (Duke Math. J. 2021)
  2. Arithmetic intersections of modular geodesics (J. Number Theory 2022)
  3. Real quadratic Borcherds products (Pure Appl. Math. Q. 2022)

  It computes rigid meromorphic theta cocycles, their RM values, their cuspidal values, as well as Stark–Heegner points on elliptic curves.

• Overconvergent modular forms

  This code builds on the code of Alan Lauder, and some parts of it were also written jointly with him. It has three main branches, which compute:

  1. Spaces of overconvergent modular forms for any prime p, as well as routines to compute eigenforms, projections, and Chow–Heegner points on elliptic curves. Computing overconvergent forms for small primes (LMS J. Comp. 2015)
  2. Spaces of overconvergent modular forms at the boundary of weight space. Modular eigenforms at the boundary of weight space (Res. Number Theory 2018)
  3. p-Adic L-functions of totally real fields (with A. Lauder). Computing p-adic L-functions of totally real fields (Math. Comp. 2022)

• Quadratic Chabauty

  The following code, building crucially on code written by Jan Tuitman, is based on the following papers with Jennifer Balakrishnan, Netan Dogra, Steffen Müller, and Jan Tuitman:

  1. Explicit Chabauty–Kim for the split Cartan modular curve of level 13 (Ann. Math. 2019)
  2. Quadratic Chabauty for modular curves (Compos. Math. 2023)