physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
higher geometry / derived geometry
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
function algebras on ∞-stacks?
derived smooth geometry
This page collects pointers related to the conference and book project:
Gabriel Catren, Mathieu Anel, (eds.)
New Spaces for Mathematics and Physics
conference (IHP Paris, Oct-Sept 2015)
and
New spaces in mathematics: formal and conceptual reflections,
Cambridge University Press (2021)
ISBN:9781108854429
on current developments regarding foundations of geometry in mathematics and physics.
Patrick Iglesias-Zemmour on diffeological spaces.
Pierre Schapira on microlocal analysis.
On topology and algebraic topology.
On Grothendieck toposes regarded as “logoses”:
Michel Vaquié on sheaves and functorial geometry.
Carlos Simpson on algebraic stacks.
On derived geometry.
Maxim Kontsevich on derived noncommutative geometry in terms of formal duals of dg-categories (stable infinity-categories, enhanced triangulated categories, see also at spectrum of a triangulated category).
On noncommutative geometry and supergeometry.
Alain Connes on spectral geometry.
Klaas Landsman on Bohr toposes.
Mikhail Kapranov on superalgebra as sphere spectrum-graded algebra (see also at spectral super-scheme):
Mikhail Kapranov, Supergeometry in mathematics and physics, in Gabriel Catren, Mathieu Anel, (eds.) New Spaces for Mathematics and Physics (arXiv:1512.07042)
Mikhail Kapranov, Super-geometry, talk at New Spaces for Mathematics & Physics, IHP Paris, Oct-Sept 2015 (video recording)
On derived symplectic geometry:
On higher prequantum geometry:
On spacetime.
On the continuum:
On twistors:
Marcos Mariño on AdS-CFT duality.
Anders Kock on synthetic differential geometry
Jean Pradines on Lie groupoids
Patrick Iglesias-Zemmour on diffeological spaces.
(lecture notes pdf)
Michel Vaquié on sheaves and gros toposes.
Carlos Simpson on algebraic stacks and the Artin representability theorem.
Mathieu Anel on derived geometry (pdf)
Maxim Kontsevich on derived noncommutative geometry in terms of formal duals of stable infinity-categories (enhanced triangulated categories, see also at spectrum of a triangulated category).
Shahn Majid on noncommutative geometry
Timothy Porter on thinking of spaces as infinity groupoids and the relation with the homotopy hypothesis.
(video recording) (draft of article)
Denis-Charles Cisinski on motives.
Damien Calaque, Derived stacks in symplectic geometry (arXiv:1802.09643)
Hanno Sahlmann on spin networks.
Mikhail Kapranov on superalgebra as sphere spectrum-graded algebra (see also at spectral super-scheme).
Mikhail Kapranov, Supergeometry in mathematics and physics, in Gabriel Catren, Mathieu Anel, (eds.) New Spaces for Mathematics and Physics (arXiv:1512.07042)
Mikhail Kapranov, Super-geometry, talk at New Spaces for Mathematics & Physics, IHP Paris, Oct-Sept 2015 (video recording)