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

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

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

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

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

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

Simulating the molecular structure of materials under pressures so extreme that we are not yet able to study them in the laboratory.

Extending the theory of thermodynamics to account for quantum mechanics and the optimisation of energy transfer in quantum systems.

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

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

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

Creating discrete models of space that obey Euclid’s axioms over long distances and open up new possibilities for non-continuum physics.

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

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.

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

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

Creating powerful mathematical methods for predicting cancer outcomes that can be coded in algorithms for fast parallel processing.

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

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

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

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

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

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 aggregation.

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.

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

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