### Available:*

Library | Call Number | Material Type | Home Location | Status |
---|---|---|---|---|

Central Library | QC20.7.G44 G463 1998 | Adult Non-Fiction | Central Closed Stacks | Searching... |

### On Order

### Summary

### Summary

This 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 importantresearchers, 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-commutativegeometry, 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 ofquantum 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.

### Author Notes

Mathematical Institute, 24-29 St Giles', OXFORD, OX1 3LB. Tel: +44 1865 273525; fax: +44 1865 273583

### Reviews 1

### Choice Review

Internationally renowned theoretical physicist Penrose invented twistor theory, a radical new approach to space-time where geometric points no longer enter the theory as primitives. More recently, he has stirred controversy with two books that invoke modern physics to plumb the nature of human consciousness. This festschrift honoring Penrose on his 65th birthday contains survey articles by some of the most eminent mathematicians (Atiyah, Donaldson, Connes, et al.) and physicists (Hawking, Astekar, Veneziano, among others) of our time. Besides browsing the most formidable contributions, undergraduates may particularly benefit from Artur Ekert's introduction to quantum cryptography, Paul Steinhardt's new approach to Penrose tilings, and particularly, biologist Stuart Hameroff's defense of Penrose's theories of consciousness from the charge of merely constituting a "minimization of mysteries." Highly recommended. Undergraduates through faculty. D. V. Feldman; University of New Hampshire

### Table of Contents

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 |