New Spaces for Mathematics and Physics




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics


on current developments regarding foundations of geometry in mathematics and physics.


1. Smoothness and singularities

Schemes (Pierre Cartier)

Pierre Cartier on schemes.

(video recording)

Synthetic differential geometry - new methods for old spaces (Anders Kock)

Anders Kock on synthetic differential geometry

(video recording)

Lie (or differentiable) groupoids (Jean Pradine)

Jean Pradines on Lie groupoids

(video recording)

Diffeologies (Patrick Iglesias-Zemmour)

Patrick Iglesias-Zemmour on diffeological spaces.

(video recording)

(lecture notes pdf)

2. Spaces with categories of points

Geometric aspects of topos theory in relation with logical doctrines (André Joyal)

André Joyal on topos theory.

(video recording)

Sheaves and functors of points (Michel Vaquié)

Michel Vaquié on sheaves and gros toposes.

Stacks and the Artin property (Carlos Simpson)

Carlos Simpson on algebraic stacks and the Artin representability theorem.

(video recording)

The Geometry of Ambiguity: An introduction to the ideas of Derived Geometry (Mathieu Anel)

Mathieu Anel on derived geometry (pdf)

(video recording)

3. Non-commutative geometry

Geometry from statistical physics and information theory (Matilde Marcolli)

Geometry in triangulated categories (Maxim Kontsevich)

Maxim Kontsevich on derived noncommutative geometry in terms of formal duals of stable infinity-categories (enhanced triangulated categories).

Quantum differential geometry (Shahn Majid)

Shahn Majid on noncommutative geometry

4. Spaces up to homotopy

Spaces as infinity-groupoids (Timothy Porter)

Timothy Porter on the homotopy hypothesis-theorem.

(video recording)

Homological decomposition and motives (Denis-Charles Cisinski)

Denis-Charles Cisinski on motives.

(video recording)

Homotopy type theory: the logic of homotopy spaces (Mike Shulman)

Mike Shulman on homotopy type theory (arXiv:1703.03007)

5. Spaces in classical & quantum mechanics

Derived stacks in symplectic geometry (Damien Calaque)

Damien Calaque on derived symplectic geometry (arXiv:1802.09643)

Higher pre-quantized geometry (Urs Schreiber)

Urs Schreiber on Higher Prequantum Geometry.

(arXiv:1601.05956, video recording)

Cobordisms and extended quantum field theories (Dan Freed)

Dan Freed on extended TQFT and the cobordism hypothesis.

Notion of space in topos quantum theory (Cecilia Flori)

Cecilia Flori on Bohr toposes.

6. Spaces in quantum gravity

Spin networks and spinfoams (Hanno Sahlmann)

Hanno Sahlmann on spin networks.

(video recording)

Super-geometry (Mikhail Kapranov)

Mikhail Kapranov on superalgebra as sphere spectrum-graded algebra.

Twistor theory (Roger Penrose)

Roger Penrose on twistors.

(video recording)

Stringy geometry and emergent space (Marcos Mariño)

Marcos Mariño on AdS-CFT

(video recording)

7. Open questions

What experiments tell us about space and time (John Baez)

John Baez on experiments.

Time between real and imaginary: what geometries describe the Universe near the Big Bang? (Yuri Manin)

Yuri Manin on Wick rotation in cosmology.

category: reference

Last revised on June 13, 2018 at 04:42:13. See the history of this page for a list of all contributions to it.