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New Spaces in Physics
Formal and Conceptual Reflections

Volume 2


  • Editors:
  • Mathieu Anel, Carnegie Mellon University, Pennsylvania
  • Gabriel Catren, Centre National de la Recherche Scientifique (CNRS), Paris
Mathieu Anel, Gabriel Catren, Alain Connes, Klaas Landsman, Mikhail Kapranov, Damien Calaque, Urs Schreiber, John C. Baez, Roger Penrose, Muxin Han, Marcos Mariño
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  • Date Published: April 2021
  • availability: In stock
  • format: Hardback
  • isbn: 9781108490627

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About the Authors
  • After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.

    • An introduction to a vast array of notions of 'space' in mathematics and physics, suitable for graduates and researchers
    • Addressed to mathematicians and mathematical physicists, but also suitable for historians and philosophers of these disciplines
    • Includes chapters written by leading mathematicians and theoretical physicists (including two Fields Medallists)
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    Reviews & endorsements

    'The collection would be of interest to any physicist, mathematician, historian, or philosopher seeking a survey of the approaches to dealing with the modern concept of space in physics … Recommended.' E. Kincanon, Choice Magazine

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    Product details

    • Date Published: April 2021
    • format: Hardback
    • isbn: 9781108490627
    • length: 1 pages
    • dimensions: 235 x 157 x 29 mm
    • weight: 0.73kg
    • contains: 22 b/w illus. 1 table
    • availability: In stock
  • Table of Contents

    Introduction Mathieu Anel and Gabriel Catren
    Part I. Noncommutative and supercommutative geometries:
    1. Noncommutative geometry, the spectral standpoint Alain Connes
    2. The logic of quantum mechanics (revisited) Klaas Landsman
    3. Supergeometry in mathematics and physics Mikhail Kapranov
    Part II. Symplectic geometry:
    4. Derived stacks in symplectic geometry Damien Calaque
    5. Higher prequantum geometry Urs Schreiber
    Part III. Spacetime:
    6. Struggles with the continuum John C. Baez
    7. Twistor theory: a geometric perspective for describing the physical world Roger Penrose
    8. Quantum geometry of space Muxin Han
    9. Stringy geometry and emergent space Marcos Mariño.

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    New Spaces in Physics

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  • Editors

    Mathieu Anel, Carnegie Mellon University, Pennsylvania
    Mathieu Anel is a Visiting Assistant Professor at Carnegie Mellon University. His research interests include higher category theory, algebraic topology, and topos theory.

    Gabriel Catren, Centre National de la Recherche Scientifique (CNRS), Paris
    Gabriel Catren is Permanent Researcher in philosophy of physics at the French National Centre for Scientific Research (CNRS). His research interests include the foundations of classical and quantum mechanics, and the foundations of gauge theories.


    Mathieu Anel, Gabriel Catren, Alain Connes, Klaas Landsman, Mikhail Kapranov, Damien Calaque, Urs Schreiber, John C. Baez, Roger Penrose, Muxin Han, Marcos Mariño

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