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I will report on a work in progress with Federico Lo Bianco, Erwan Rousseau, and Frédéric Touzet about the structure of codimension one foliations having an infinite group of birational symmetries.

37F75 ; 32S65 ; 14E05

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37F75

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14E30 ; 14J32 ; 32J27

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14E30 ; 14J32 ; 32J27

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The decomposition theorem gives some insight on the structure of compact Kähler manifolds with trivial first Chern class. In the first part of the talk I will try to summarize the history of the problem, from the Calabi conjecture to its proof by Yau; in the second part I will explain why the result is an easy consequence of Yau's theorem.

14J32 ; 53C26

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The purpose of the discussion session is to discuss how the proof of the decomposition theorem came to be

14-06

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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.[-]

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 ...[+]

53D17 ; 37F75 ; 14J10

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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.[-]

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 ...[+]

37F75 ; 53D17 ; 14J10

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Documents Pereira, Jorge Vitório 37 résultats

Rational curves and contraction loci on symplectic manifolds - Amerik, Ekaterina (Auteur de la conférence) | CIRM H Nouveau

Birational transformations preserving codimension one foliations - Pereira, Jorge Vitório (Auteur de la conférence) | CIRM H Nouveau

A splitting theorem - Druel, Stéphane (Auteur de la conférence) | CIRM H Nouveau

Structure theory for singular varieties with trivial canonical divisor - Greb, Daniel (Auteur de la conférence) | CIRM H Nouveau

Holonomy of singular Ricci-flat metrics - Guenancia, Henri (Auteur de la conférence) | CIRM H Nouveau

The decomposition theorem: the smooth case - Beauville, Arnaud (Auteur de la conférence) | CIRM H Nouveau

Interview at CIRM: Jorge Vitório Pereira - Pereira, Jorge Vitório (Personne interviewée) ; Vareilles, Stéphanie (Intervieweur) | CIRM H Nouveau

Varieties with Trivial Canonical Class: discussion session - Pereira, Jorge Vitório (Animateur) | CIRM H Nouveau

Holomorphic Poisson structures - lecture 1 - Pym, Brent (Auteur de la conférence) | CIRM H Nouveau

Holomorphic Poisson structures - lecture 2 - Pym, Brent (Auteur de la conférence) | CIRM H Nouveau