Holomorphic Poisson structures - lecture 1 | Vidéo | Carmin.tv

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Holomorphic Poisson structures - lecture 1

Apparaît dans la collection : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a particle is trapped.

I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.

Informations sur la vidéo

Date de captation 27/04/2020
Date de publication 29/04/2020
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19630303
Citer cette vidéo Pym, Brent (27/04/2020). Holomorphic Poisson structures - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19630303
URL https://dx.doi.org/10.24350/CIRM.V.19630303

Domaine(s)

Bibliographie

POLISHCHUK, A. Algebraic geometry of Poisson brackets. Journal of Mathematical Sciences, 1997, vol. 84, no 5, p. 1413-1444. - https://doi.org/10.1007/BF02399197
PYM, Brent. Constructions and classifications of projective Poisson varieties. Letters in mathematical physics, 2018, vol. 108, no 3, p. 573-632. - https://doi.org/10.1007/s11005-017-0984-5
DUFOUR, Jean-Paul et ZUNG, Nguyen Tien. Poisson structures and their normal forms. Springer Science & Business Media, 2006. - https://doi.org/10.1007/b137493
LAURENT-GENGOUX, Camille, PICHEREAU, Anne, et VANHAECKE, Pol. Poisson structures. Springer Science & Business Media, 2012. - https://doi.org/10.1007/978-3-642-31090-4

Codes MSC

Document(s)

https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-cirm_poisson_discussion.pdf

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