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Early history of symplectic geometry / by Grodecz Alfredo Ramírez Ogando. Wuppertal, April 22, 2022
Content
Introduction
Symplectic Group
Symplectic group
Marius Souphous Lie
Emergence of Symplectic Groups
Weyl and the Symplectic group
Symplectic Geometry by Siegel
Carl Ludwig Siegel
Symplectic geometry by Siegel
Siegel Modular forms
Quadratic forms
Analytical interpretation
Siegel modular functions of degree n
Symplectic geometry 1943
Reception of Siegel's paper 1943
Siegel's and Hua's parallel works
Hua Loo-Keng
Hua in Europe
Remarks on Siegel's and Hua's parallel work
Differential forms
Symplectic form and symplectic space
Differential forms
Élie Cartan
Cartan differential form
Closed differential forms
Early applications of differential forms
Kähler form - Symplectic form
Erich Kähler
Kähler Metric
Reception of Kähler manifolds
Eckmann and Guggenheimer
Eckmann and Guggenheimer's work on Kähler manifolds
Symplectic Manifolds
Ehresmann and Feldbau
Jacques Feldbau
Symplectic Manifolds
Fibre Spaces, Fibre Bundle
Almost complexes structures
Ehresmann: Symplectic Manifolds
The first reception and the relation between symplectic manifolds and Kähler manifolds
Siegel's Half Space is a Symplectic Manifold
Darboux's theorem
Two versions of Darboux's theorem
The form used in symplectic geometry
The classical form
A look back to the late 19th century
Pfaffian's Problem
Gaston Darboux
The classical theorem of Darboux
The perspective of symplectic manifolds
Paulette Libermann
Equivalence between symplectic structures
About the name of Darboux's Theorem
Symplectic Geometry-Lee Hwa-Chung
About Lee Hwa-Chung Live
Even dimensional geometry
Even dimensional manifolds endowed with a nonsingular closed 2-form (Symplectic manifold)
Conformal flat manifolds
Automorphisms
Poisson bracket
Hamilton's equations
Equivalence of flat spaces
Lee Hwa Chung Theorem
The reception of Lee's work
Classical Mechanics
Classical Mechanics
Lagrangian and Hamiltonian Mechanics
Symplectic Group and Classical Mechanics
Aurel Wintner and Canonical Transformations
Aurel Wintner
Canonical Transformations
Lectures on Celestial Mechanics
Georges Reeb Systémes Dynamiques
George Reeb
Systèmes Dynamiques
Colloque de Géométrie Différentielle
Basic mathematical concepts
Lagrangian subspace
Submanifolds of a Symplectic Manifold
About the Name: Lagrangian Subspaces
Symplectomorphisms
Strasbourg 1953
Géométrie symplectique différentielle
Jean-Marie Souriau
Differential Symplectic Geometry and applications
Vector Space and Symplectic Vector Space
Phase space
Géométrie Symplectique Différentielle
Les Transformations Canoniques - Sympletomorphisms
Applications
Take off
Symplectic geometry takes off
Foundations of mechanics
Symplectic geometry conferences in 1973 and 1974
Textbooks and journals about symplectic geometry
Conclusion
Appendices
Shiing-Shen Chern
Chern and Erich Kähler
Chern and Élie Cartan
Gauss-Bonnet Theorem
Vladimir Arnold
Arnold's conjecture
Symplectic topology
Liste of participants
Geometria simplettica
Géométrie Symplectique
Bibliography