We revel in using mathematics to understand the world and improve it. Our expanding space of research projects—in physics, mathematics, AI, life, technology, finance and beyond—reflects the interests of our scientists. They are funded by grants and donors from across the globe.
Systemic risk
Applying ideas from diversification and cascading failures to mitigate the propagation of risk across inter-connected institutions.
At the edge of crystals
Capturing in simulations and mathematical form the surface structure of crystals and how they coalesce when heated but not melted.
Economic complexity
Applying spectral-like theories to the bipartite network of products and capabilities to find latent potential in countries and firms.
Collective creativity
Understanding collective creativity: anonymous collaboration under constrained freedom that transcends the creativity of the individual.
Extreme pressure surprises
Simulating the molecular structure of materials under pressures so extreme that we are not yet able to study them in the laboratory.
Fractal heat exchange
Designing optimal self-similar structures for compact counter-current heat exchange to reduce heating costs and greenhouse emissions.
Fractal structures
Using fractal, or self-similar, patterns to design the lightest possible load-bearing structures with new strength-to-mass scaling laws.
Fundamental advances in AI
Developing radical new approaches to inference and automated decision making using advances in quantum information and statistical physics.
Alternative universes
Taming limitations of general relativity, such as the big bang singularity, by formulating theories that admit bouncing or cyclic universes.
Inference in many dimensions
Developing a theory of high-dimensional statistical inference using analytic tools from the statistical physics of disordered systems.
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.
Bootstrap percolation
Advancing the mathematical theory of bootstrap percolation, where active cells on a lattice with few active neighbours cease to be active.
Sense from social networks
Developing new local and global measures for networks derived from social interactions to infer social structure, sentiment and behaviour.
Markets and the mind
Examining the effect of public opinion on stock market returns and harnessing social sentiment to make quantitative market predictions.
Dimension extension
Reconstructing the 3D shape distribution of rock grains or other randomly packed objects with access to only a 2D slice through them.
Mathematical medicine
Creating powerful mathematical methods for predicting the outcomes of diseases that pinpoint the right treatments and speed up drug trials.
News and fake news
Investigating the adverse effects of information asymmetry and deliberate errors in social media and the press, and attempts to remedy them.
Puzzles in packing
Predicting the geometry and behaviour of densely packed objects from first principles, from spheres to polydisperse spheres to cells.
Spectre of hypercubes
Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.
Reconstructing credit networks
Using ideas from statistical physics to reconstruct the average properties of financial networks from partial sets of information.
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.
Remembering to learn
Understanding the dynamics of networks of memristors, a new paradigm for low-power computation inspired by the structure of the brain.
Repairable instead of robust
Developing a new approach to resilience in which mistakes and unexpected events are mitigated by easy repairs rather than redundancy.
Reprogramming the cell
Applying mathematical tools to the holy grail of cellular biology: can we produce every type of human cell from within the laboratory?
Surprises from simple rules
Understanding complex dynamical behaviours generated by simple rules, such as cellular automata, polyominoes and models of competition.
Intelligence of graphs
Predicting the behaviour of graphs and processes on them by treating topological patterns as constraints on a random graph ensemble.
Technological progress
Forecasting the rate of technological progress by harnessing empirical regularities captured by Moore’s law and Wright’s law.
The structure of innovation
Creating a mathematical model of combinatorial innovation to understand how innovation rates can be influenced as components are acquired.
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.
Information thermodynamics
Understanding the physical nature of information and how it relates to energy transfer and new technologies that make use of these insights.