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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  • Mahler measuring the genetic code of amoebae

    Algebraic geometry

    SCYHY. HeEHANAZ In Press Advances in Theoretical and Mathematical Physics

    Mahler measuring amoebae

    Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.

  • Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces

    Algebraic geometry

    AAYHY. HeEHBA Arxiv

    Bundled Laplacians

    By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.

  • John Keith Stuart McKay: 1939-2022

    Group theory

    YHY. He Submitted

    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.

  • Clustering cluster algebras with clusters

    AI-assisted maths

    MCPDYHY. HeEHEH... In Press Advances in Theoretical and Mathematical Physics

    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.

  • 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

    Physics Letters B

    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

    Journal of High Energy Physics

    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

    Physics Letters B

    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


    AI for cluster algebras

    Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

  • AI-assisted maths

    Physics Letters B

    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

    Physical Review D

    Calabi-Yau anomalies

    Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.

  • String theory

    Communications in Mathematical Physics

    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

    Journal of Symbolic Computation

    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

    International Journal of Modern Physics A

    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

    Unifying Mahler measure, dessins and gauge theory, Newton polynomials reveal a 1-to-1 correspondence between Mahler measure and dessins.

  • String theory

    Journal of High Energy Physics

    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

    Journal of Symbolic Computation

    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.