Recent advances in diffeologies and their applications : AMS EMS SMF Special Session$dRecent Advances in Diffeologies and Their Applications July 18 20 2022 Université de Grenoble Alpes Grenoble France On diffeologies from infinite dimensional geometry to PDE constrained optimization Nico Goldammer Jean Pierre Magnot and Kathrin Welker Elastic diffeological spaces Christian Blohmann A remark on stability and D topology of mapping space Alireza Ahmadi Smooth maps on convex sets Yael Karshon and Jordan Watts A survey on diffeological vector spaces and applications Enxin Wu Finite dimensional diffeological vector spaces being and not being coproducts Ekatarina Pervova Singular foliations through diffeologies David Miyamoto Diffeological coarse moduli spaces of stacks over manifolds Jordan Watts and Seth Wolbert Generalized Laurent monomials in nonrational toric varieties Fiametta Battaglia and Elisa Prato On a remark by Alan Weinstein Iakovos Androulidakis Diffeologies and generalized Kadomtsev Petviashvili hierarchies Anahita Elsami Rad Jean Pierre Magnot Enrique G. Reyes and Vladimir Rubtsov Smooth A[infinity] forms on diffeological loop space Norio Iwase Smooth homotopy of diffeological spaces : theory and application to infinite dimensional C[infinity] manifolds Hiroshi Kihara.