Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
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AI-assisted maths
PDYH
EHEH J Comput AlgebraAI for cluster algebras
Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.
Algebraic geometry
AAYH
EHBA Journal of High Energy PhysicsBundled Laplacians
By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.
Algebraic geometry
PBYH
EHEHVJ... Physics Letters BGenetic polytopes
Genetic algorithms, which solve optimisation problems in a natural selection-inspired way, reveal previously unconstructed Calabi-Yau manifolds.
Algebraic geometry
SCYH
EHANAZ Advances in Theoretical and Mathematical Physics, in press Mahler measuring amoebae
Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.
Group theory
On John McKay
This obituary celebrates the life and work of John Keith Stuart McKay, highlighting the mathematical miracles for which he will be remembered.
AI-assisted maths
AI for arithmetic curves
AI can predict invariants of low genus arithmetic curves, including those key to the Birch-Swinnerton-Dyer conjecture—a millennium prize problem.
AI-assisted maths
Clustered cluster algebras
Cluster variables in Grassmannian cluster algebras can be classified with HPC by applying the tableaux method up to a fixed number of columns.
Number theory
Elliptic curve murmurations
Certain properties of the bivariate cubic equations used to prove Fermat’s last theorem exhibit flocking patterns, machine learning reveals.
Evolvability
Flowers of immortality
The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.
Gravity
AI classifies space-time
A neural network learns to classify different types of spacetime in general relativity according to their algebraic Petrov classification.
String theory
Algebra of melting crystals
Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.
AI-assisted maths
Machine learning Hilbert series
Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.
AI-assisted maths
Line bundle connections
Neural networks find numerical solutions to Hermitian Yang-Mills equations, a difficult system of PDEs crucial to mathematics and physics.
AI-assisted maths
Calabi-Yau anomalies
Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.
String theory
Mahler measure for quivers
Mahler measure from number theory is used for the first time in physics, yielding “Mahler flow” which extrapolates different phases in QFT.
AI-assisted maths
Learning the Sato–Tate conjecture
Machine-learning methods can distinguish between Sato-Tate groups, promoting a data-driven approach for problems involving Euler factors.
Machine learning
Universes as big data
Machine-learning is a powerful tool for sifting through the landscape of possible Universes that could derive from Calabi-Yau manifolds.
Number theory
Reflexions on Mahler
With physically-motivated Newton polynomials from reflexive polygons, we find the Mahler measure and dessin d’enfants are in 1-to-1 correspondence.
String theory
QFT and kids’ drawings
Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.
Machine learning
Neurons on amoebae
Machine-learning 2-dimensional amoeba in algebraic geometry and string theory is able to recover the complicated conditions from so-called lopsidedness.
Group theory
New approaches to the Monster
Editorial of the last set of lectures given by the founder, McKay, of Moonshine Conjectures, the proof of which got Borcherds the Fields Medal.