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 book project,
Cambridge University Press 2019
(toc pdf)
on current developments regarding foundations of geometry in mathematics and physics.
I.1. Differential geometry I.1.1 Diffeologies (Patrick Iglesias-Zemmour) I.1.2 New methods for old spaces: synthetic differential geometry (Anders Kock) I.1.3 Microlocalanalysis and beyond (Pierre Schapira)
I.2. Topology and algebraic topology I.2.1 Topo-logie (Mathieu Anel & André Joyal) (pdf) I.2.2 Spaces as infinity-groupoids (Timothy Porter) I.2.3 Homotopy type theory: the logic of space (Mike Shulman)
I.3. Algebraic geometry I.3.1 Sheaves and functors of points (Michel Vaquié) I.3.2 Stacks (Nicole Mestrano & Carlos Simpson) I.3.3 The geometry of ambiguity – An introduction to derived geometry (Mathieu Anel) I.3.4 Geometry in dg-categories (Maxim Kontsevich)
II.1. Non-commutative and super-commutative geometries II.1.1 Noncommutative Geometry, the spectral standpoint (Alain Connes) II.1.2 Topos quantum theory (Klaas Landsman) II.1.3 Super-geometry (Mikhail Kapranov)
II.2. Symplectic geometry II.2.1 Derived stacks in symplectic geometry (Damien Calaque) II.2.2 Higher pre-quantized geometry (Urs Schreiber)
II.3. Space-time II.3.1 Struggles with the Continuum (John Baez) II.3.2 Twistor theory (Roger Penrose) II.3.3 Loop quantum gravity (Muxin Han) II.3.4 Stringy geometry and emergent space (Marcos Mariño)
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).
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.
Mike ShulmanHomotopy type theory: the logic of space (arXiv:1703.03007)
(on homotopy type theory)
Damien Calaque on derived symplectic geometry (arXiv:1802.09643)
Urs Schreiber on Higher Prequantum Geometry.
(arXiv:1601.05956, video recording)
Hanno Sahlmann on spin networks.
Mikhail Kapranov on superalgebra as sphere spectrum-graded algebra.
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)
John Baez on experiments.
Last revised on February 8, 2020 at 12:48:12. See the history of this page for a list of all contributions to it.