This book presents recent advances in topics related to Poisson geometry originating from lectures given at the Poisson School held in 2022 at the CRM in Barcelona. The purpose is to give both an introduction to this active field of research as well as highlight new trends in related topics. The texts cover both classical results, known to experts in the field, as well as recent and previously unpublished mathematical results.

Graduate students and early-stage researchers with basic knowledge in differential and symplectic geometry, together with established researchers that are keen to dive into this rapidly growing field of research, will find this book a useful resource.

Covers material that was completely ignored in the current literature Unites several articles in a single work Includes exercise sets that will especially be useful for graduate students

Autorentext

Mario Garcia-Fernandez is a permanent researcher (Científico Titular) at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid., from January 2024.

David Iglesias Ponte is professor in Geometry and Topology at the University of La Laguna since 2019.

Eva Miranda is a Full Professor in Geometry and Topology at UPC and CRM-Barcelona, Alexander Von Humboldt Friedrich Wilhelm Bessel professor at Mathematisches Institut der Universität zu Köln.

Cédric Oms is currently a Post-doc at the BCAM in Bilbao, Spain.

Roberto Rubio is a Ramón y Cajal fellow at the Department of Mathematics of the Universitat Autónoma de Barcelona since July 2022.

Inhalt

• Part I: Introduction to Poisson Geometry. - 1. A brief Introduction to Poisson Geometry.- Part II: Wonderful Varieties. - 2. Wonderful Varieties with a View Towards Poisson Geometry.- Part III: An Invitation to Singular Foliations. - 3. What is a singular foliation?.- 4. Canonical geometric and algebraic structures hidden behind a singular foliation.- 5. State of the Art and open questions.