2024-2025
Research
Published
-
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 ] -
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
-
Learning Euler Factors of Elliptic Curves
with Angelica Babei, François Charton, Steve Huang, Kyu-Hwan Lee, David Lowry-Duda, Ashvni Narayanan, and
to appear in Advances in Theoretical and Mathematical Physics
[ arXiv ] -
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 ] -
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 ] -
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 ] -
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
-
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 ] -
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
-
Rigorous computation of Picard lattices of quartic K3 surfaces
with Emre Can Sertöz -
Computing the isogeny class of any principally polarized abelian surface over the rationals
with Raymond van Bommel, Shiva Chidambaram, and Jean Kieffer -
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 ] -
Kodaira dimension of Hilbert modular threefolds via Fourier expansions
with Eran Assaf, Adam Logan, and Sam Schiavone
[ Code ]
Talks
-
Explicit modularity of K3 surfaces with CM of large degree
[
slides
]
LMFDB, Computation, and Number Theory (LuCaNT)
July 2025 -
Effective Computation of Hodge Cycles
[
slides
]
Columbia-CUNY-NYU number theory seminar
April 2025 -
17T7 is a Galois group over the rationals
[
slides
]
Joint meeting of the AMS, AustMS and NZMS: Computational Number Theory
December 2025 -
Effective Computation of Hodge Cycles
[
slides
]
Computational Algebra Seminar, University of Sydney
November 2024 -
Computing L-functions
[
slides
code
]
Murmurations in Arithmetic Geometry and Related Topics, SUNY
November 2024 -
AGNES Scavenger Hunt with Magma
[
slides
code
]
Algebraic Geometry Northeastern Series, Dartmouth College
November 2024 -
Machine learning L-functions
[
slides
]
Mathematics and Machine Learning, Harvard
October 2024 -
Effective Computation of Picard lattices of K3 surfaces
[
slides
]
Explicit Methods in Number Theory, Oberwolfach
September 2024 -
Effective Computation of Hodge Cycles
[
slides
]
Geometry Over Non-Closed Fields, Simons Symposium, Elmau
August 2024 -
Hypergeometric L-functions in average polynomial time, II
[
slides
code
]
Algorithmic Number Theory Symposium XVI, MIT
July 2024
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
andpolredbest
so that the endomorphisms package no longer depends onPARI/GP
.
- Implement
- Revisit Jupyter integration and explore the following options:
magma -x
- xeus
- 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.