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New Spaces in Mathematics and Physics 2 Volume Hardback Set

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New Spaces in Mathematics and Physics 2 Volume Hardback Set

New Spaces in Mathematics and Physics 2 Volume Hardback Set

Formal and Conceptual Reflections
Mathieu Anel , Carnegie Mellon University, Pennsylvania
Gabriel Catren , University Paris Diderot
April 2021
Available
Multiple copy pack
9781108854368

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£93.00
GBP
Multiple copy pack
2 Hardback books
    Description

    After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. These books 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. They are addressed primarily to mathematicians and mathematical physicists, 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)

    Product details

    April 2021
    Multiple copy pack
    9781108854368
    900 pages
    235 × 157 × 67 mm
    1.7kg
    42 b/w illus. 31 tables
    Available

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    Contents

    Table of Contents

    • Volume 1: Introduction Mathieu Anel and Gabriel Catren
    • Part I. Differential geometry:
    • 1. An Introduction to diffeology Patrick Iglesias-Zemmour
    • 2. New methods for old spaces: synthetic differential geometry Anders Kock
    • 3. Microlocal analysis and beyond Pierre Schapira
    • Part II. Topology and algebraic topology:
    • 4. Topo-logie Mathieu Anel and André Joyal
    • 5. Spaces as infinity-groupoids Timothy Porter
    • 6. Homotopy type theory: the logic of space Michael Shulman
    • Part III. Algebraic geometry:
    • 7. Sheaves and functors of points Michel Vaquié
    • 8. Stacks Nicole Mestrano and Carlos Simpson
    • 9. The geometry of ambiguity: an introduction to the ideas of derived geometry Mathieu Anel
    • 10. Geometry in dg categories Maxim Kontsevich
    • Volume 2: Introduction Mathieu Anel and Gabriel Catran
    • Part I. Noncommutative and super-commutative 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 programme 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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    Additional Information
    About the authors
      Contributors

    • Mathieu Anel, Gabriel Catren, Patrick Iglesias-Zemmour, Anders Kock, Pierre Schapira, André Joyal, Timothy Porter, Michael Shulman, Michel Vaquié, Nicole Mestrano, Carlos Simpson, Maxim Kontsevich, Alain Connes, Klaas Landsman, Mikhail Kapranov, Damien Calaque, Urs Schreiber, John C. Baez, Roger Penrose, Muxin Han, Marcos Mariño

      • 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 , University Paris Diderot

      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.

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