Introduction to Symplectic Geometry

Jean Louis Koszul, born in 1921, was a French Mathematician. He was a member of 2nd generation of Bourbaki, also a member of French Academy of Sciences.  Jean-Louis Koszul passed away on January 12th 2018, at the age of 97.

“This book is of great interest for the emerging field of Geometric Science of Information, in which the generalization of the Fisher metric is at the heart of the extension of classical tools from Machine Learning and Artificial Intelligence to deal with more abstract objects living in homogeneous manifolds, groups, and structured matrices.’” (Pablo Suárez-Serrato, zbMATH 1433.53002, 2020)

• Some Algebra Basics.- Symplectic Manifolds.- Cotangent Bundles.- Symplectic G-spaces.- Poisson Manifolds.- A Graded Case.