Number theory and computation
Research
My mathematical work centers on explicit arithmetic: modular forms, elliptic curves, the Birch and Swinnerton-Dyer conjecture, and software that makes difficult computation broadly accessible.
Current research / 2026
Rebuilding Sage for mathematical agents
Sage.js is my active research project with Codex: a from-scratch open mathematical system designed so agents have excellent software for serious mathematics and can help extend the system itself.
It connects the original SageMath mission, the explicit number theory below, and two decades of browser-based collaborative computing in CoCalc. The new constraint is agent legibility: readable implementations, precise semantics, executable documentation, independent mathematical oracles, and evidence for every maturity claim.
Areas
Three connected threads
Each guide selects durable entry points from the larger archive: representative writing, books, talks, and computational data.
Modular forms and modular abelian varieties
Explicit arithmetic of modular forms, modular symbols, Hecke algebras, and the abelian varieties attached to them.
Explore the work 02 / Arithmetic geometryElliptic curves and the BSD conjecture
Computation and conjectures surrounding elliptic curves, modular abelian varieties, ranks, and Shafarevich-Tate groups.
Explore the work 03 / Computation and softwareOpen mathematical software for humans and agents
Algorithms, databases, and open systems for doing mathematics reproducibly, collaboratively, and with computational agents.
Explore the workComplete record
Writing, data, and people
The thematic pages are intentionally selective. These catalogs preserve the broader output and the people and funding that supported it.