New Spaces in Mathematics and Physics 2 Volume Hardback Set

Formal and Conceptual Reflections
Erscheinungsjahr 2021
ISBN: 978-1-108-85436-8
Verlag: Cambridge University Press

Buch, Englisch, 900 Seiten, Format (B × H): 158 mm x 235 mm, Gewicht: 1668 g

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.

Autoren/Hrsg.

Anel, Mathieu

Catren, Gabriel

Fachgebiete

• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

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

Catren, Gabriel
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.