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.→
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.
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.