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

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.→

Developing a mathematical theory of how trust trees grow and how we can traverse them to exploit trust corridors in society for searching.→

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.→

## Artificial intelligence of graphs

Developing intelligent inference by treating topological patterns in graphs and networks as constraints on a random graph ensemble.

## 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.

## Deducing three dimensions from two

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

## 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.

## Is technology a machine for creating itself?

Developing a statistical physics model of recursive innovation in which technologies become the building blocks for new technologies.

## 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.