2024-2025

Research

Published

  1. Hypergeometric L-functions in average polynomial time, II
    with Kiran Kedlaya, and David Roe
    Sixteenth Algorithmic Number Theory Symposium, Research in Number Theory 11, 32 (2025)
    [ arXiv DOI Offprint Code MR ]
  2. Abelian varieties of prescribed order over finite fields
    with Raymond van Bommel, Wanlin Li, Bjorn Poonen, and Alexander Smith
    Mathematische Annalen, Volume 392, pages 1167–1202, (2025)
    [ arXiv DOI Code ]

To appear

  1. Learning Euler Factors of Elliptic Curves
    with Angelica Babei, François Charton, Xiaoyu Huang, Kyu-Hwan Lee, David Lowry-Duda, Ashvni Narayanan, and
    to appear in Advances in Theoretical and Mathematical Physics
    [ arXiv ]
  2. Explicit modularity of K3 surfaces with complex multiplication of large degree
    with Andreas-Stephan Elsenhan, Jörg Jahnel, and John Voight
    to appear in LMFDB, Computation, and Number Theory (LuCaNT)
    [ arXiv Code ]
  3. Curve equations from expansions of 1-forms at a nonrational point
    with Raymond van Bommel, Bjorn Poonen, and Padmavathi Srinivasan
    to appear in LMFDB, Computation, and Number Theory (LuCaNT)
    [ arXiv ]
  4. Labeling abelian varieties over finite fields
    with Taylor Dupuy, Stefano Marseglia, David Roe, and Christelle Vincent
    to appear in LMFDB, Computation, and Number Theory (LuCaNT)
    [ arXiv Code ]
  5. Learning Fricke signs from Maass form Coefficients
    with Joanna Bieri, Girgi Butbaia, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra
    to appear in Advances in Theoretical and Mathematical Physics
    [ arXiv ]

Submitted

  1. Machine learning the vanishing order of rational $L$-functions
    with Joanna Bieri, Girgi Butbaia, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, and Tamara Veenstra
    [ arXiv ]
  2. 17T7 is a Galois group over the rationals
    with Raymond van Bommel, Noam D. Elkies, Timo Keller, Sam Schiavone, and John Voight
    [ arXiv Code ]

In progress

  1. Rigorous computation of Picard lattices of quartic K3 surfaces
    with Emre Can Sertöz
  2. Computing the isogeny class of any principally polarized abelian surface over the rationals
    with Raymond van Bommel, Shiva Chidambaram, and Jean Kieffer
  3. Computing with Fourier expansions of Hilbert modular forms
    with Eran Assaf, Angelica Babei, Ben Breen, Sara Chari, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Abhijit Mudigonda, Sam Schiavone, and John Voight
    [ Code ]
  4. Kodaira dimension of Hilbert modular threefolds via Fourier expansions
    with Eran Assaf, Adam Logan, and Sam Schiavone
    [ Code ]

Talks

Magma

Website

Made progress toward a minimal Flask app that will replace the existing PHP website.

Documentation system

Investigated alternative documentation infrastructures for Magma.

Continuous integration and automation

Explored options for enabling continuous integration for the Magma project.

2025-2026 Goals

Research

  • Complete the papers listed in the ‘In progress’ section.

  • Begin a paper that uses $p$-adic differential equations to compute zeta functions of plane curves.

  • Revisit a decade old project with David Harvey on computing zeta functions of projective hypersurfaces over finite fields.

  • Revisit making Kuga–Satake constructions explicit when a K3 surface is given as a double cover of $\mathbb{P}^2$ branched over six lines, by making Paranjape’s work explicit.

Magma

Website

Replace the main website, retaining legacy components only where necessary.

Documentation system

Begin migrating the documentation to a modern system, most likely Sphinx.

Code

  • Add several basic utilitarian tools for the major release:
    • Implement Sequence/List/Set/MultiSet/IndexedSet/… functions that convert an iterable object into the requested type.”
    • Provide a generic FromString(MntStg, Typ) -> Typ to convert basic format types from strings.
    • Additional utilities already prototyped in CHIMP
    • Develop alternatives to polredabs and polredbest so that the endomorphisms package no longer depends on PARI/GP.
  • Revisit Jupyter integration and explore the following options:
  • Release an alpha version of a package manager.

Organization

Set up a public bug tracker.

Automation

  • Establish full continuous integration forcompilation and testing.

  • Investigate applying the same CI pipeline to releases.

  • Explore providing nightly releases.

Development environment

  • Enable public pull requests for package code.