4 papers
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…
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…