The elegant universe
What are the ultimate causes of the universe? In the reductionist tradition, we tackle the synthesis of the fundamental forces, and the nature of symmetry, causality and information. We also develop new mathematics that unify these and other fields that at first seem unconnected.
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 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.
Exploring the spectral properties of subgraphs of the hypercube and Hamming graphs for insights into coding theory and models of evolution.
Generalizing the divisor function to find a new kind of number that can be recursively divided into parts, for use in design and technology.
Understanding the physical nature of information and how it relates to energy transfer and new technologies that make use of these insights.