New Spaces in Mathematics and Physics 2 Volume Hardback Set
Formal and Conceptual Reflections

In these graduate-level books, leading researchers explore various new notions of 'space' in mathematics and mathematical physicists.

Mathieu Anel (Edited by), Gabriel Catren (Edited by)

9781108854368, Cambridge University Press

Multiple-component retail product, published 1 April 2021

900 pages, 42 b/w illus. 31 tables
23.5 x 15.7 x 6.7 cm, 1.7 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Philosophy of science [PDA], Topology [PBP], Geometry [PBM]