There are many wonderful connections between mathematics and physics. The discovery and exploration of the fundamental laws of nature involves deep mathematical ideas, and several of the most important current themes of research in mathematics were stimulated by questions and concepts coming from physics.
We are interested in a range of areas of research connecting mathematics and physics. One involves the statistical behaviour of complex systems. In the case of classical systems, we seek to understand how simple collective behaviour emerges from complex interactions; in complex quantum systems, we study the influence of chaos and integrability, and connections with the theory of random matrices. Random matrix theory is related to a wide range of areas of mathematics and science, extending from biology to quantum gravity. We are particularly interested in connections with number theory, including the behaviour of the Riemann zeta function. Bristol has a long and distinguished history of contributions to quantum chaos, random matrix theory, and developing connections with number theory; several foundational ideas were developed here. Research in these areas is frequently done in collaboration with members of the other Institutes in the School.
Quantum Mechanics is a fascinating and important physical theory. Many of the most significant technological developments of the past century have at their heart novel quantum phenomena, which often relate to deep ideas in mathematics. There is currently a considerable focus on the interrelations between quantum mechanics and information theory, and on consequences for computation, thermodynamics and other areas of science. Again, researchers in Bristol, who form a highly collaborative community stretching across several departments, have made major contributions to the foundations of this area of research.
Former students in the School include Paul Dirac, and discoveries made in Bristol at the interface between mathematics and physics include the Aharonov-Bohm effect, the Geometric (‘Berry’) Phase, universal statistical properties of quantum chaotic systems, and several of the most striking consequences of quantum entanglement.