The elegant universe
Tackling big questions about the fundamental forces, symmetry and information, and the intimate interplay between physics and mathematics.
We lack a single theory that describes the universe. Gravity, described by general relativity, is not consistent with quantum field theory describing the other three forces. Will this be resolved by string theory, loop quantum gravity, or something new? What are the testable consequences of such a theory, which is currently beyond the limits of human experimentation? We seek the structure of the extra dimensions of space-time whose geometry determines our universe.
We study the large-scale structure of space-time, especially in relation to singularities. Can black hole thermodynamics help prescribe a theory of everything? What are the implications of the holographic principle? What is behind dark energy and matter, which are posited to make sense of the cosmos?
We study the physical nature of information, and the extraction of energy from fluctuations in the environment. We seek a foundational understanding of the relation between information and energy in the classical and quantum regimes.
Wigner noted the unreasonable effectiveness of mathematics in physics. Today, we see the reverse: attempts to advance physics, such as string theory, are driving mathematics. We investigate the convergence between pure mathematics and fundamental physics, and how this vantage could help redress physics’ current impasse.
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.