Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each one is the result of many months of research, so we make a special effort to make our papers clear, inspiring and beautiful, and publish them in leading journals.

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  • T. FinkT. Fink
  • O. GamayunO. Gamayun
  • A. EsterovA. Esterov
  • Y. HeY. He
  • F. SheldonF. Sheldon
  • A. V. KosyakA. V. Kosyak
  • A. OchirovA. Ochirov
  • E. SobkoE. Sobko
  • M. BurtsevM. Burtsev
  • M. ReevesM. Reeves
  • I. ShkredovI. Shkredov
  • G. CaldarelliG. Caldarelli
  • R. HannamR. Hannam
  • F. CaravelliF. Caravelli
  • A. CoolenA. Coolen
  • O. DahlstenO. Dahlsten
  • A. MozeikaA. Mozeika
  • M. BardosciaM. Bardoscia
  • P. BaruccaP. Barucca
  • M. RowleyM. Rowley
  • I. TeimouriI. Teimouri
  • F. AntenucciF. Antenucci
  • A. ScalaA. Scala
  • R. FarrR. Farr
  • A. ZegaracA. Zegarac
  • S. SebastioS. Sebastio
  • B. BollobásB. Bollobás
  • F. LafondF. Lafond
  • D. FarmerD. Farmer
  • C. PickardC. Pickard
  • T. ReevesT. Reeves
  • J. BlundellJ. Blundell
  • A. GallagherA. Gallagher
  • M. PrzykuckiM. Przykucki
  • P. SmithP. Smith
  • L. PietroneroL. Pietronero
  • AI-driven research in pure mathematics and theoretical physics

    AI-assisted maths

    YHY. He Nature Reviews Physics

    On AI-driven discovery

    Reviewing progress in the field of AI-assisted discovery for maths and theoretical physics reveals a triumvirate of different approaches.

  • Generating triangulations and fibrations with reinforcement learning

    AI-assisted maths

    PBGBYHY. HeEHEH... Arxiv

    Triangulating polytopes

    Machine learning generates desirable triangulations of geometric objects that are required for Calabi-Yau compactification in string theory.

  • Machine Learning Clifford invariants of ADE Coxeter elements

    AI-assisted maths

    SCPDYHY. HeEHEH... Advances in Applied Clifford Algebras

    Clifford invariants by ML

    Coxeter transformations for root diagrams of simply-laced Lie groups are exhaustively computed then machine learned to very high accuracy.

  • Cluster algebras: network science and machine learning

    AI-assisted maths

    PDYHY. HeEHEH J Comput Algebra

    AI 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

    Journal of High Energy Physics

    Bundled Laplacians

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

  • AI-assisted maths

    Physics Letters B

    Computing Sasakians

    Topological quantities for the Calabi-Yau link construction of G2 manifolds are computed and machine learnt with high performance scores.

  • Algebraic geometry

    Physics Letters B

    Genetic polytopes

    Genetic algorithms, which solve optimisation problems in a natural selection-inspired way, reveal previously unconstructed Calabi-Yau manifolds.

  • Algebraic geometry

    Advances in Theoretical and Mathematical Physics

    Analysing amoebae

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

  • Group theory

    Bulletin of the London Mathematical Society, in press

    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

    Journal of Symbolic Computation

    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

    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.

  • Number theory

    Experimental Mathematics

    Elliptical murmurations

    Certain properties of the bivariate cubic equations used to prove Fermat’s last theorem exhibit flocking patterns, machine learning reveals.

  • String theory

    Physics Letters B

    World in a grain of sand

    An AI algorithm of few-shot learning finds that the vast string landscape could be reduced by only seeing a tiny fraction to predict the rest.

  • Evolvability

    Arxiv

    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

    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

    Submitted

    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

    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

    ICCM

    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.