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.

## Hidden communities

Employing theoretical measures to detect communities and connections in complex networks.

## Organising a defence

Using both theory and experimental analyses to understand how the immune system responds to an alien invasion such as coronavirus.

## 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.

## Learning the universe

Using machine learning methods to search the vast space of Calabi-Yau manifolds for ones that predict the Standard Model from string theory.

## 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.

## The fate of real systems

Improving our understanding of real-world networks with sophisticated analyses of realistic complications.

## 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.