New Spaces in Physics: Formal and Conceptual Reflections

Naslovnica
Mathieu Anel, Gabriel Catren
Cambridge University Press, 2021 - Broj stranica: 436
"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. Mathieu Anel is Assistant Professor at Carnegie Mellon University. His research interests include higher category theory, topos theory, and symplectic geometry. 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)"--
 

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New Spaces in Physics
5
Contents for New Spaces in Mathematics
9
Contents for New Spaces in Mathematics page vii
15
Acknowledgments
18
DIFFERENTIAL GEOMETRY
29
An Introduction to Diffeology 31
61
Synthetic Differential Geometry
83
The Logic of Quantum Mechanics Revisited
85
Derived Stacks in Symplectic Geometry
155
Higher Prequantum Geometry
202
Spaces as InfinityGroupoids
258
Struggles with the Continuum
281
The Logic of Space
322
7
327
Muxin
373
Marcos Mariño
407

Supergeometry in Mathematics and Physics
114
Microlocal Analysis and Beyond
117

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O autoru (2021)

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 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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