We revel in using mathematics to understand the world and improve it. Our expanding space of research projects—in physics, mathematics, AI, technology, finance and beyond—reflects the interests of our scientists. They are funded by grants and donors from across the globe.

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

Reconstructing the 3d shape distribution of grains or other objects randomly packed together with access only to 2d slices through them.→

Understanding collective creativity: anonymous collaboration under constrained freedom that transcends the creativity of the individual.→

Developing a theory of high-dimensional statistical inference using analytic tools from the statistical physics of disordered systems.→

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

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

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

Creating powerful mathematical methods for predicting the outcomes of diseases that pinpoint the right treatments and speed up drug trials.→

Designing optimal self-similar structures for compact counter-current heat exchangers to reduce heating costs and greenhouse emissions. →

Predicting the geometry and behaviour of densely packed objects in the natural and man-made worlds, from rocks to foams to spheres.→

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

Developing a new approach to resilience in which mistakes and unexpected events are mitigated by easy repairs rather than redundancy.→

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

Forecasting the rate of technological progress by harnessing empirical regularities captured by Moore’s law and Wright’s law.→

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

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

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

## At the surface of crystals

Capturing in simulations and mathematical form the surface structure of crystals and how they coalesce when heated but not melted.

## Building blocks of economic complexity

Applying spectral-like theories to the bipartite network of products and capabilities to find latent potential in countries and firms.

## Extracting meaning from social networks

Developing new local and global measures for networks derived from social interactions to infer social structure, sentiment and behaviour.

## 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.

## Fundamental advances in machine learning

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

## How to remember currents and voltages

Understanding the dynamics of memristor networks, a new approach to low-power computation inspired by the structure of the brain.

## Implications of alternative universes

Taming limitations of general relativity, such as the big bang singularity, by formulating theories that admit bouncing or cyclic universes.

## Markets and the mind

Examining the effect of public opinion on stock market returns and harnessing social sentiment to make quantitative market predictions.

## News and fake news in a connected world

Investigating the adverse effects of information asymmetry and deliberate errors in social media and the press and attempts to remedy them.

## Reconstructing a credit network

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

## What to do when failure is contagious

Applying ideas from diversification and cascading failures to mitigate the propagation of risk across inter-connected institutions.