346 citations · 1k across the 42 of their papers we have counts for
45 papers
Smyth's conjecture and a non-deterministic Hasse principle
Jordan S. Ellenberg, Will Hardt
In a 1986 paper, Smyth proposed a conjecture about which integer-linear relations were possible among Galois-conjugate algebraic numbers. We prove this conjecture. The main tools (…
Generative Modeling for Mathematical Discovery
Jordan S. Ellenberg, Cristofero S. Fraser-Taliente, Thomas R. Harvey +2
We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some…
Certifying nontriviality of Ceresa classes of curves
Jordan Ellenberg, Adam Logan, Padmavathi Srinivasan
The Ceresa cycle is a canonical algebraic -cycle on the Jacobian of an algebraic curve. We construct an algorithm which, given a curve over a number field, often provides a cert…
PatternBoost: Constructions in Mathematics with a Little Help from AI
François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner +1
We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a clas…
Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields
Jordan S. Ellenberg, Aaron Landesman
We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer groups of quadratic twist families of abelian varieties over global function fields. As a consequ…
Sparsity of Integral Points on Moduli Spaces of Varieties
Jordan S. Ellenberg, Brian Lawrence, Akshay Venkatesh
Let be a quasi-projective variety over a number field, admitting (after passage to ) a geometric variation of Hodge structure whose period mapping has zero-dimensio…