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Accueil du site > Projets de recherche financés en cours > Projet ERC Philosophie de la Gravitation Quantique Canonique > Séminaire de philosophie et physique-mathématique 2015-2016 > Seminar of Philosophy and mathematical physics 2014–2015

Seminar of Philosophy and mathematical physics 2014–2015

ERC PROJECT PHILOSOPHY OF CANONICAL QUANTUM GRAVITY

Presentation,
Research Axes
Practical Information
Members Calls for application
Seminar
"(Id)entity :: (Id)entification"
Events


Working Group of the Project, organisation : Gabriel Catren, Mathieu Anel, Julien Page, Federico Zalamea (CNRS and Univ. Paris Diderot, SPHERE)
Contact : gabriel.catren((at))univ-paris-diderot.fr


To current year
Archives : 2015–2016, 2013–2014, 2012–2013


Working Group on Stacks
organised by Mathieu Anel

June 2015
30/06/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Groupe de travail sur les Champs IX (Stacks)
23/06/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Groupe de travail sur les Champs VIII (Stacks)
9/06/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Groupe de travail sur les Champs VII (Stacks)
2/06/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Groupe de travail sur les Champs VI (Stacks)
May 2015
26/05/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Working Group on Stacks V
19/05/2015
Tues. 10:00
Room Alechinsky, 437A Mathieu Anel Working Group on Stacks IV
6/05/2015
Wed. 14:30
Room Alechinsky, 437A Mathieu Anel Working Group on Stacks III
April 2015
28/04/2015
Tues. 10:00
Room Klein, 371A Mathieu Anel Working Group on Stacks II
21/04/2015
Tues. 10:00
Room Klein, 371A Mathieu Anel Working Group on Stacks I)

Programme :
Fields in groupoids are generalizations of the notion of differentiable and algebraic variety. The purpose of this working group will be to understand the definition of a field including the notion of sheaf. We will follow a course for that of Bertrand Toén ( link below) .
List of things you will see :

  • Varieties and beams ( Toén Chapter 1 & 2)
  • Heory of homotopy groupoid ( Toén Chapter 5, Hollander, Dugger . )
  • Groupoids and rustic beams down condition ( Toén end chap 5)
  • Fibered categories ( Vistoli )
  • Equivalence between categories and fibered in groupoids presheaves ( Hollander )
  • Sheaves

References :
– Dugger, D., A primer on homotopy colimits
– Hollander, S., A homotopy theory for stacks
– Toën, B., A master course on algebraic stacks
– Vistoli, A., Notes on Grothendieck topologies, fibered categories and descent theory


December 2014
12/12/2014
vendredi 14:00
room Mondrian, 646A Mathieu Anel Towards Symplectic Stacks VI
09/12/2014
mardi 14:00
room Kandinsky, 631B Mathieu Anel Towards Symplectic Stacks V
November 2014 (usually on Mon. and Thurs.)
27/11/2014
Thurs. 10:00
room Mondrian, 646A Urs Schreiber Higher geometric quantization IV
Quantization of Chern-Simons-type field theories
24/11/2014
Mon. 14:00
room Gris, 734A Mathieu Anel Towards Symplectic Stacks IV
 !! 21 !!//11/2014
Thurs. 10:00
room Gris, 734A Urs Schreiber Higher geometric quantization III
Quantizaton of Poisson manifolds
17/11/2014
Mon. 14:00
room Gris, 734A Mathieu Anel Towards Symplectic Stacks III
14/11/2014
Fri. 10:00
room Gris, 734A Urs Schreiber Higher geometric quantization III
Formulating geometric quantization
10/11/2014
Mon. 14:00
room Gris, 734A Mathieu Anel Towards Symplectic Stacks II
06/11/2014
Thurs. 10:00
room Kandinsky, 631B Urs Schreiber Higher geometric quantization I
Basics of higher differential geometry
03/11/2014
Mon. 14:00
room Gris, 734A Mathieu Anel Towards Symplectic Stacks I


Abstracts :


03–24/11/2014 Towards Symplectic Stacks
by Mathieu Anel (ERC project PhiloQuantumGravity, CNRS)
The purpose of this course is to introduce the notion of "stack", which is an extension of the notion of manifold that takes care about possible symmetries of objects. Manifolds, or wannabe manifolds, are constructed (from other manifolds) by taking subspaces (defined by some equations) and/or by taking quotients (often defined by some group action). However these operations usually create singularities that prevent the result to be a manifold. We shall focus on the construction of quotients and explain how to enhance the definition of manifold into that of differentiable stack, so that it can become stable by quotients. In a second part we shall define differential forms on stacks and their symplectic structure, introducing to ideas of Toën, Pantev, Vaquié and Vezzosi. During the different lectures, we shall discuss in particular the following notions :
  1. Groupoids, homotopy types, classifying space of a group and cohomology
  2. Functor of points, moduli problems, Grothendieck topologies, sheaves and stacks
  3. Tangent complex, symplectic structures, symplectic groupoids


Bibliography :




06–27/11/2014 Higher geometric quantization
by Urs Schreiber (Invited researcher in the context of ERC project PhiloQuantumGravity)
This lecture series begins with a basic introduction to concepts of higher (stacky) differential geometry. Then I introduce an elegant formulation of traditional geometric quantization via such concepts. As a first application, I explain a natural geometric quantization of compact Poisson manifolds, extending the familiar quantization of symplectic manifolds. I close with an outlook on aspects of the geometric quantization of Chern-Simons type field theories.

  1. Lecture 1 : Basics of higher differential geometry
  2. Lecture 2 : Formulating geometric quantization
  3. Lecture 3 : Quantization of Poisson manifolds
  4. Lecture 4 : Quantization of Chern-Simons-type field theories


Bibliography : Notes accompanying the lectures are here.
















This project has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) for research, technological development and demonstration under grant agreement n° 263523 (Project Philosophy of Canonical Quantum Gravity)