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Book DetailsContemporary MathematicsVolume: 794; 2024; 258 ppMSC: Primary 14; 37; 46; 49; 53; 57; 58; 81
This volume contains the proceedings of the AMSEMSSMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de GrenobleAlpes, 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.
ReadershipGraduate students and research mathematicians interested in topology, differential geometry, and functional analysis.

Table of Contents

Articles

Nico Goldammer, JeanPierre Magnot and Kathrin Welker — On diffeologies from infinite dimensional geometry to PDE constrained optimization

Christian Blohmann — Elastic diffeological spaces

Alireza Ahmadi — A remark on stability and the Dtopology of mapping spaces

Yael Karshon and Jordan Watts — Smooth maps on convex sets

Enxin Wu — A survey on diffeological vector spaces and applications

Ekaterina Pervova — Finitedimensional diffeological vector spaces being and not being coproducts

David Miyamoto — Singular foliations through diffeology

Jordan Watts and Seth Wolbert — Diffeological coarse moduli spaces of stacks over manifolds

Fiammetta Battaglia and Elisa Prato — Generalized Laurent monomials in nonrational toric geometry

Iakovos Androulidakis — On a remark by Alan Weinstein

Anahita EslamiRad, JeanPierre Magnot, Enrique G. Reyes and Vladimir Rubtsov — Diffeologies and generalized KadomtsevPetviashvili hierarchies

Norio Iwase — Smooth $A_{\infty }$form on a diffeological loop space

Hiroshi Kihara — Smooth homotopy of diffeological spaces: theory and applications to infinitedimensional $C^\infty $manifolds


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This volume contains the proceedings of the AMSEMSSMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de GrenobleAlpes, 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.
Graduate students and research mathematicians interested in topology, differential geometry, and functional analysis.

Articles

Nico Goldammer, JeanPierre Magnot and Kathrin Welker — On diffeologies from infinite dimensional geometry to PDE constrained optimization

Christian Blohmann — Elastic diffeological spaces

Alireza Ahmadi — A remark on stability and the Dtopology of mapping spaces

Yael Karshon and Jordan Watts — Smooth maps on convex sets

Enxin Wu — A survey on diffeological vector spaces and applications

Ekaterina Pervova — Finitedimensional diffeological vector spaces being and not being coproducts

David Miyamoto — Singular foliations through diffeology

Jordan Watts and Seth Wolbert — Diffeological coarse moduli spaces of stacks over manifolds

Fiammetta Battaglia and Elisa Prato — Generalized Laurent monomials in nonrational toric geometry

Iakovos Androulidakis — On a remark by Alan Weinstein

Anahita EslamiRad, JeanPierre Magnot, Enrique G. Reyes and Vladimir Rubtsov — Diffeologies and generalized KadomtsevPetviashvili hierarchies

Norio Iwase — Smooth $A_{\infty }$form on a diffeological loop space

Hiroshi Kihara — Smooth homotopy of diffeological spaces: theory and applications to infinitedimensional $C^\infty $manifolds