The elegant universe

Tackling big questions about the fundamental forces, symmetry and information, and the intimate interplay between physics and mathematics.

General relativity and quantum field theory are among physics’ greatest triumphs. One describes gravity as the geometry of spacetime; the other describes matter and the remaining three fundamental forces. Both are confirmed to many decimal places, and each fails where the other cannot be ignored. Reconciling them is the deepest open problem in physics.

The Standard Model, our quantum theory of these particles and forces, leaves some of nature’s most basic patterns unexplained. Why do quarks and leptons come in three families, and why do their masses differ so widely? What is dark matter? What explains the pattern of particles and charges that cancels otherwise fatal gauge anomalies? We explore these questions through connections with condensed-matter physics and the search for a deeper framework that unites matter and gravity in a single quantum description.

Gravity brings its own puzzles, from the singularities predicted by general relativity to the dark energy associated with the universe's accelerating expansion. Black holes need gravity and quantum theory at once, and neither suffices. Their predicted evaporation appears to destroy what quantum evolution must preserve. We study what black-hole thermodynamics reveals about spacetime, and the wider relationship between information and matter—from the physical cost of erasing information to the role of quantum entanglement in the emergence of spacetime itself.

String theory and its proposed extension, M-theory, offer a possible route to a single quantum description of matter and gravity and dualities are central to this picture — two theories that look nothing alike can describe the same world. These surprising equivalences can connect strong interactions to weak ones; holography even relates a world with gravity to a lower-dimensional one without it. They raise a deeper question: could spacetime itself emerge from quantum physics? We explore these connections within exactly solvable models, where special symmetries make exact answers possible—offering rare footholds for testing ideas about nature’s underlying laws.

The search for exact solutions and hidden symmetries also opens new paths in pure mathematics. Wigner noted the unreasonable effectiveness of mathematics in physics. The reverse now holds too, and the hunt for exact solutions and hidden symmetries is driving pure mathematics, to the point where ideas from quantum theory now furnish new proofs of classical theorems in geometry. We investigate that convergence and take it as a guide: our aim is a description of nature in which the mathematics is not merely adequate but inevitable.

  • Machine learning the regulatory structure of cell states

    Learning the cell-state space

    Building machine learning models that mimic the behaviour of cells in silico to improve the prediction of genes for cell programming.

  • Mathematics of immortality

    Deriving the mortality equation, which governs the dynamics of an ageing population, and solving it to crack the evolutionary origin of ageing.

  • Informative experiment design

    Developing the mathematical structure of experiments using information theory and combinatorics to speed up the discovery of new cell types.

  • Theory of genetic computation

    Understanding genetic computation using regulatory motifs, a new kind of structural and functional building block of gene regulatory networks.

  • Learning the universe

    Using machine learning to search the vast space of 10-dimensional geometries for ones that predict the Standard Model from string theory.

  • Recursively divisible numbers

    Generalizing the divisor function to find a new kind of number that can be recursively divided into parts, for use in design and technology.

  • Fundamental advances in AI

    Developing radical new approaches to inference and automated decision making using advances in quantum information and statistical physics.

  • The structure of innovation

    Creating a mathematical model of combinatorial innovation to understand how innovation rates can be influenced as components are acquired.

  • Bootstrap percolation

    Advancing the mathematical theory of bootstrap percolation, where active cells on a lattice with few active neighbours cease to be active.

  • Surprises from simple rules

    Understanding complex dynamical behaviours generated by simple rules, such as cellular automata, polyominoes and models of competition.

  • Fractal structures

    Using fractal, or self-similar, patterns to design the lightest possible load-bearing structures with new strength-to-mass scaling laws.

  • Structure of how things relate

    Creating mathematical tools for characterizing the structure of ideal graphs and irregular networks, and the behaviour of processes on them.

  • Reconstructing credit networks

    Using ideas from statistical physics to reconstruct the average properties of financial networks from partial sets of information.

  • Information thermodynamics

    Understanding the physical nature of information and how it relates to energy transfer and new technologies that make use of these insights.

  • Spectre of hypercubes

    Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.

  • Puzzles in packing

    Predicting the geometry and behaviour of densely packed objects from first principles, from spheres to polydisperse spheres to cells.

  • Is continuous space illusory?

    Creating discrete models of space and spacetime that appear continuous over long lengths and set the stage for non-continuum physics.

  • Remembering to learn

    Understanding the dynamics of networks of memristors, a new paradigm for low-power computation inspired by the structure of the brain.

  • Intelligence of graphs

    Predicting the behaviour of graphs and processes on them by treating topological patterns as constraints on a random graph ensemble.