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New Spaces in Mathematics
Formal and Conceptual Reflections

Volume 1

$69.99 (C)

  • Editors:
  • Mathieu Anel, Carnegie Mellon University, Pennsylvania
  • Gabriel Catren, Centre National de la Recherche Scientifique (CNRS), Paris
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
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  • Date Published: June 2021
  • availability: In stock
  • format: Hardback
  • isbn: 9781108490634

$ 69.99 (C)

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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. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is 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)
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    Reviews & endorsements

    ‘The essays are self-contained, providing motivation to read selectively. Examples in each chapter illustrate the usefulness of these new notions of space … Recommended.’ M. Clay, Choice Magazine

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    Product details

    • Date Published: June 2021
    • format: Hardback
    • isbn: 9781108490634
    • length: 550 pages
    • dimensions: 234 x 156 x 37 mm
    • weight: 0.94kg
    • contains: 20 b/w illus. 30 tables
    • availability: In stock
  • Table of Contents

    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.

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    New Spaces in Mathematics

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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, Patrick Iglesias-Zemmour, Anders Kock, Pierre Schapira, André Joyal, Timothy Porter, Michael Shulman, Michel Vaquié, Nicole Mestrano, Carlos Simpson, Maxim Kontsevich

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