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New Spaces in Mathematics

New Spaces in Mathematics
Formal and Conceptual Reflections

Volume 1

c.£54.99

  • 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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  • Publication planned for: August 2020
  • availability: Not yet published - available from August 2020
  • format: Hardback
  • isbn: 9781108490634

c.£ 54.99
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  • Mathematicians have long known that geometry is not absolute. Our understanding of what constitutes a 'space' has driven, and been driven by, significant applications inside and outside of mathematics. The workshop 'New Spaces in Mathematics and Physics', held in 2015 at the Institut Henri Poincaré, brought together many researchers to discuss various new notions of space in mathematics and theoretical physics, with particular attention given to often overlooked aspects of their subjects, conceptual reflections and historical perspectives. This volume and its companion New Spaces in Physics arise from their lectures and discussions. This volume covers 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.

    • Introduces a vast array of notions of 'space' in mathematics and physics, suitable for graduates and researchers
    • Includes a mixture of formal introductions and more conceptual reflections, historical perspectives, and current open problems
    • Contains chapters written by leading mathematicians and theoretical physicists (including two Fields Medallists)
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    Product details

    • Publication planned for: August 2020
    • format: Hardback
    • isbn: 9781108490634
    • dimensions: 228 x 152 mm
    • contains: 20 b/w illus. 30 tables
    • availability: Not yet published - available from August 2020
  • 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.

  • Editors

    Mathieu Anel, Carnegie Mellon University, Pennsylvania
    Mathieu Anel is Assistant Professor at Carnegie Mellon University. His research interests include higher category theory, topos theory, and symplectic geometry.

    Gabriel Catren, Centre National de la Recherche Scientifique (CNRS), Paris
    Gabriel Catren is Permanent Researcher at the French National Centre for Scientific Research (CNRS). His main areas of research are the foundations of classical and quantum mechanics, and the foundations of gauge theories (general relativity and Yang–Mills theories).

    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

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