Book project

This conference is part of the wider project of editing a collective book. The workshop is conceived as an opportunity to collectively discuss and enrich the different contributions to the book.

Table of Contents (Preliminary Version)

1. Reimagining topology and differential geometry

1. 1. Diffeologies (Patrick Iglesias-Zemmour)  
   2. Synthetic dierential geometry - new methods for old spaces (Anders Kock)
   3. Geometric aspects of topos theory in relation with logical doctrines (André Joyal)
   4. Micro-local analysis and beyond (Pierre Schapira)

2. Functorial approach to geometry

1. 1. Schemes (Pierre Cartier) 
   2. Sheaves and functors of points (Michel Vaquié)
   3. Stacks and the Artin property (Carlos Simpson & Nicole Mestrano)
      
   4. Derived geometry (Mathieu Anel)

 3. Spaces up to homotopy

1. 1. Spaces as infinity-groupoids (Timothy Porter)
   2. Homotopy type theory: the logic of homotopy spaces (Mike Shulman)

4. Non-commutative geometry

1. Geometry in dg-categories (Maxim Kontsevich)
2. Noncommutative Geometry, the spectral standpoint (Alain Connes)

5. Spaces in classical & quantum physics

1. Derived stacks in symplectic geometry (Damien Calaque)
2. Higher pre-quantized geometry (Urs Schreiber)
3. Topos quantum theory (Klaas Landsman)
4. What experiments tell us about space and time (John Baez)
   

6. Spaces in quantum gravity

1. Loop quantum gravity (Muxin Han)
2. Super-geometry (Mikhail Kapranov)
3. Stringy geometry and emergent space(Marcos Mariño)
   
4. Twistor theory (Roger Penrose)