This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18-20, 2022, at the Universite de Grenoble-Alpes, Grenoble, France.
The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE.
The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.
N. Goldammer, J.-P. Magnot, and K. Welker, On diffeologies from infinite
dimensional geometry to PDE constrained optimzation
C. Blohmann, Elastic diffeological spaces
A. Ahmadi, A remark on stability and the D-topology of mapping spaces
Y. Karshon and J. Watts, Smooth maps on convex sets
E. Wu, A survey on diffeological vector spaces and applications
E. Pervova, Finite-dimensional diffeological vector spaces being and not
being coproducts
D. Miyamoto, Singular foliations through diffeology
J. Watts and S. Wolbert, Diffeological coarse moduli spaces of stacks over
manifolds
F. Battaglia and E. Prato, Generalized Laurent monomials in nonrational toric
geometry
I. Androulidakis, On a remark by Alan Weinstein
A. Eslami-Rad, J.-P. Magnot, E. G. Reyes, and V. Rubtsov, Diffeologies and
generalized Kadomtsev-Petviashvili hierarchies
N. Iwase, Smooth $A_\infty$-form on a diffeological loop space
H. Kihara, Smooth homotopy of diffeological spaces: Theory and applications
to infinite-dimensional $C^\infty$-manifolds
Jean-Pierre Magnot, Universite d'Angers, France.
Lycee Jeanne d'Arc, Clermont-Ferrand, France.
