Huggett S.A., Mason L.J., Tod., Tsou S.T., Woodhouse N.M.J. (Eds.) The Geometric Universe: Science, Geometry, and the Work of Roger Penrose

Oxford University Press, New York, USA, 1998. – 444 p. – ISBN: 0198500599This collection has been inspired by the work of Roger Penrose. It gives an overview of current work on the interaction between geometry and physics, from which many important developments in research have emerged. This volume collects together the contributions of many important researchers, including Sir Roger himself, and gives an overview of the many applications of geometrical ideas and techniques across mathematics and the physical sciences. From the area of pure mathematics papers are included on the topics of classical differential geometry and non-commutative geometry, knot invariants, and the applications of gauge theory. Contributions from applied mathematics cover the topics of integrable systems and general relativity. Current research in experimental and theoretical physics inspired chapters on string theory, quantum gravity, the foundations of quantum mechanics, quasi-crystals and astrophysics. The collection also includes articles on quantum computation, quantum cryptography and the possible role of micro-tubules in a theory of consciousness.Plenary Lectures
Roger Penrose—A Personal Appreciation
Hypercomplex Manifolds and the Space of Framings
Gauge Theory in Higher Dimensions
Noncommutative Differential Geometry and the
Einstein's Equation and Conformai Structure
Concluding remarks
On Four-Dimensional Einstein Manifolds
Loss of Information in Black Holes
Funda-mental Geometry: the Penrose-Hameroff 'Orch OR' Model of Consciousness
Implications of Transience for Spacetime Structure
Geometric Issues in Quantum Gravity
From Quantum Code-making to Quantum Code-breaking
Penrose Tilings and Quasicrystals Revisited
Decaying Neutrinos and the Geometry of the Universe
Quantum Geometric Origin of All Forces in String Theory
Space from the Point of View of Loop Groups
Quantum Theory and Beyond
The Twistor Diagram Programme
Geometric Models for Quantum Statistical Inference
Spin Networks and Topology
The Physics of Spin Networks
Geometry and Gravity
The Sen Conjecture for Distinct Fundamental Monopoles
An Unorthodox View of G R via Characteristic Surfaces
Amalgamated Codazzi-Raychaudhuri Identity for Foliation
Abstract/Virtual/Reality/Complexity
Fundamental Questions in Quantum Mechanics
Interaction-Free Measurements
Quantum Measurement Problem and the Gravitational Field
Entanglement and Quantum Computation
Mathematical Aspects of Twistor Theory
Penrose Transform for Flag Domains
Twistor Solution of the Holonomy Problem
The Penrose Transform and Real Integral Geometry
Pythagorean Spinors and Penrose Twistors
Afterword