The Geometric Universe:Science, Geometry, and the Work of Roger Penrose

图书简介

This book is a collection of articles from several world-class researchers, and is inspired by Sir Roger Penrose’s work. It gives an overview of the interaction between geometry and physics, from which many important developments have emerged. The volume collects together ideas from across the physical sciences, and indicates the many applications of geometrical ideas and techniques across mathematics and mathematical physics.

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Princeton University Library

I. PLENARY LECTURES; 1 Roger Penrose - a personal appreciation; 2 Hypercomplex manifolds and the space of framings; 3 Gauge theory in higher dimensions; 4 Noncommutative differential geometry and the structure of space-time; 5 Einstein’s equation and conformal structure; 6 Twistors, geometry, and integrable systems; 7 On four-dimensional Einstein manifolds; 8 Loss of information in black holes; 9 Fundamental geometry: the Penrose-Hameroff ’Orchor’ model of consciousness; 10 Implications of transience for spacetime structure; 11 Geometric issues in quantum gravity; 12 From quantum code-making to quantum code-breaking; 13 Penrose tilings and quasicrystals revisited; 14 Decaying neutrinos and the geometry of the universe; 15 Quantum geometric origin of all forces in string theory; 16 Space from the point of view of loop groups; II. PARALLEL SESSION I: QUANTUM THEORY AND BEYOND; 17 The twistor diagram programme; 18 Geometric models for quantum statistical inference; 19 Spin networks and topology; 20 The physics of spin networks; III. PARALLEL SESSION II: GEOMETRY AND GRAVITY; 21 The Sen conjecture for distinct fundamental monopoles; 22 An unorthodox view of CG via characteristic surfaces; 23 Amalgamated Codazzi Raychaudhuri identity for foliation; 24 Abstract/virtual/reality/complexity; IV. PARALLEL SESSION III: FUNDAMENTAL QUESTIONS IN QUANTUM MECHANICS; 25 Interaction-free measurements; 26 Quantum measurement problem and the gravitational field; 27 Entanglement and quantum computation; V. PARALLEL SESSION IV: MATHEMATICAL ASPECTS OF TWISTOR THEORY; 28 Penrose transform for flag domains; 29 Twistor solution of the holonomy problem; 30 The Penrose transform and real integral geometry; 31 Pythagorean spinors and Penrose twistors; VI. AFTERWORD; 32 Afterword

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The Geometric Universe:Science, Geometry, and the Work of Roger Penrose 数学史

The Geometric Universe:Science, Geometry, and the Work of Roger Penrose
数学史