Working Group on Diffeological Structures in Kinematic Configuration Spaces for Classical Field Theories.
Reading Seminar   8 hours
Prof. Marco Valerio D'Agostino       (INSA - Lyon )  
Prof. Alessandra Frabetti           (ICJ - Lyon )  
Dr. Antonio Michele Miti           (Sapienza - Rome )  
Configuration bundle
Where: Institut Camille Jordan
Bâtiment Jean Braconnier 21, avenue Claude Bernard, 69100
VILLEURBANNE
Room: Seminaire 1 (sous-sol) and Room 112 (first floor)
When: Autumn 2024
Contacts marco [dash] valerio [dot] dagostino [at] insa [dash] lyon [dot] fr
antoniomichele [dot] miti [at] uniroma1 [dot] it

This working group aims to establish foundational knowledge in the smooth structures of section spaces within smooth bundles, approached through the lens of diffeology.
We will use Christian Blohmann's publicly accessible lecture notes on Lagrangian Field Theories as our primary reference text.
Each session will feature an in-person lecture by a designated speaker, who will present a specific section from the reference material.
Participants are encouraged to review the assigned sections in advance, as detailed in the syllabus below.

Bibliography
  1. C. Blohmann, Lecture notes on Lagrangian Field Theories, https://people.mpim-bonn.mpg.de/blohmann/LFT/.
Syllabus
Wed 6/11/24
Seminaire 1
ICJ, sous-sol
10:30-12:00
Introduction
Motivation derived from classical field theory, classical notion of diffeological spaces with plots.
Speaker: D'Agostino
[C.Blohmann, section 1]
Tue 26/11/24
Seminaire 1
ICJ, sous-sol
10:30-12:00
Diffeological spaces as concrete sheaves
Sites, sheaves, concrete sheaves, categorical properties of diffeological spaces.
Speaker: Miti
[C.Blohmann, section 2.1]
Thu 5/12/24
Seminaire 1
ICJ, sous-sol
14:00-15:30
Diffeological tangent functor
Kan extensions, bundle of cones, representing vectors by paths.
Speaker: Frabetti
[C.Blohmann, section 2.2]
Fri 13/12/24
Room 112
ICJ
14:00-15:30
Diffeological space of fields
Mapping spaces, tangent functor of the space of fields, elastic diffeological spaces.
Speaker: TBA
[C.Blohmann, section 2.3]