339 citations · 6k across the 162 of their papers we have counts for
8 papers · 1 filter
Neurons on Amoebae
Jiakang Bao, Yang-Hui He, Edward Hirst
We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theo…
Genus One Belyi Maps by Quadratic Correspondences
Raimundas Vidunas, Yang-Hui He
We present a method of obtaining a Belyi map on an elliptic curve from that on the Riemann sphere. This is done by writing the former as a radical of the latter, which we call a qu…
Calabi-Yau Varieties: from Quiver Representations to Dessins d'Enfants
Yang-Hui He
The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror sym…
Composite Genus One Belyi Maps
Raimundas Vidunas, Yang-Hui He
Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering m…
Sporadic and Exceptional
Yang-Hui He, John McKay
We study the web of correspondences linking the exceptional Lie algebras and the sporadic simple groups Monster, Baby and the largest Fischer group. This is done via th…
Hecke Groups, Dessins d'Enfants and the Archimedean Solids
Yang-Hui He, James Read
Grothendieck's dessins d'enfants arise with ever-increasing frequency in many areas of 21st century mathematical physics. In this paper, we review the connections between dessins a…
Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces
Yang-Hui He, John McKay, James Read
We consider the 33 conjugacy classes of genus zero, torsion-free modular subgroups, computing ramification data and Grothendieck's dessins d'enfants. In the particular case of the…
Polynomial Roots and Calabi-Yau Geometries
Yang-Hui He
The examination of roots of constrained polynomials dates back at least to Waring and to Littlewood. However, such delicate structures as fractals and holes have only recently been…