7 papers
New Records for the Hadamard Maximal Determinant Problem
Giorgi Butbaia, Pragatheeswaran Vipulanandan, Justin Tan +6
The Hadamard maximal determinant problem seeks an matrix with entries in , which maximizes the determinant for a given order $n \in…
The Mathieu group is a Galois group over
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee +3
Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over during 1984-1989. We complete this program by…
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee +3
We investigate the extent to which the coefficients of the reduced minimal Weierstrass model of an elliptic curve are determined by the Diric…
Discovering a Zeta Map Algorithm on Dyck Paths via Mechanistic Interpretability
Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee
Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be ch…
On the Identification of Elliptic Curves That Admit Infinitely Many Twists Satisfying the Birch-Swinnerton-Dyer Conjecture
Barinder S. Banwait, Xiaoyu Huang
Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over for which the strong Birch-Swinner…
Learning Euler Factors of Elliptic Curves
Angelica Babei, François Charton, Edgar Costa +5
We apply transformer models and feedforward neural networks to predict Frobenius traces from elliptic curves given other traces . We train further models to predict $a_p…
Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves
Angelica Babei, Barinder S. Banwait, AJ Fong +2
We train machine learning models to predict the order of the Shafarevich-Tate group of an elliptic curve over . Building on earlier work of He, Lee, and Oliver, we show…