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UID:6745@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris;VALUE=DATE:20200518
DTEND;TZID=Europe/Paris;VALUE=DATE:20200523
DTSTAMP:20241212T135613Z
URL:https://www.i2m.univ-amu.fr/evenements/geometry-and-dynamics-of-foliat
 ions-chaire-morlet-pereira/
SUMMARY:School (CIRM\, Luminy\, Marseille): Geometry and Dynamics of Foliat
 ions (Morlet Chair - Jorge Vitorio Pereira)
DESCRIPTION:School: \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n  \n\n\n\n\n\n\n\nGeometr
 y and Dynamics of Foliations ​​\n\nMay 18-22 \n​\n​JEAN-MORLET C
 HAIR - VIRTUAL RESEARCH SCHOOL\n\nSCIENTIFIC COMMITTEE\nFrédéric Campana
  (Université de Lorraine)\nFrank Loray (CNRS-Université de Rennes I)\n
 Paulo Sad (IMPA)\n\nORGANIZING COMMITTEE\nStéphane Druel (CNRS-Universi
 té Lyon 1)\nJorge Vitório Pereira (IMPA &amp\; Aix-Marseille Universi
 té)\nErwan Rousseau (Aix-Marseille Université)\n\n\n\n\n EVENT WEBPAGE 
 \n\n\nDESCRIPTION\nFoliation Theory is a lively subject lying at a crossro
 ad of many mathematical disciplines. The School “Geometry and Dynamics 
 of Foliations” aims at presenting to young mathematicians some of the 
  different  techniques used by practitioners of the field. The topics of 
 the mini-courses give a panorama of recent developments in Foliation Theo
 ry\, ranging from algebraic-geometric to dynamical contributions.\n​\n
 ​This event  is part of  a series of three activities focusing on Foli
 ation Theory and Complex Geometry at CIRM-Luminy in 2020.\n\n\n\n\n\n\n\n\
 n\n\n\n\n\n\n\n\n\n\n\n\n\n​Dear Colleagues\, dear participants\,\n\nUnf
 ortunately\, due to the unusual circumstances\, we were forced to cancel 
 the School "Geometry and Dynamics of Foliations" in its original format. 
 We will nevertheless organize a virtual version of it.\n\nWe will record t
 he mini-courses and will make them available on this webpage before May 18
 . \n\nDuring the week which starts on May 25\, we will organize virtual 
 office hours in order to allow the participants to interact and discuss th
 e content of the mini-courses with their authors. We would also like to h
 ave some talks by young researchers this week.\n\nWe encourage the young p
 articipants of the School to submit to organisers proposal of talks (titl
 e+abstract). The talks by young participants will have 20 minutes of dura
 tion and the speakers will be able to choose whether they want their talk 
 to be recorded or not.\n\nBest regards\,\n​\nStéphane Druel\, Jorge Vit
 ório Pereira\, Erwan Rousseau\n\n\n\n\n\n\n\n\n\n\n\n\n  \n\n\n\nStéphan
 e Druel\n\n\n\n\n  \n\n\n\nJorge Vitório Pereira\n\n\n\n\n  \n\n\n\nErwan
  Rousseau\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n​TALKS AND DISCUSSI
 ON SESSIONS  \nMAY 25\, MAY 26 AND MAY 28  \n\n\n SCHEDULE ​&amp\; ABS
 TRACTS \n\n\n\n\n\n\n  \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nMINICOURSES \n\n
 \n\n\n\n\nHOLOMORPHIC POISSON STRUCTURES\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n\n\nHolomorphic Poisson Structures - Lecture 1\nBrent Pym (McGill Unive
 rsity)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Pym - Holomorphic Poisson Structures - 
 Lecture 1\n\n\n\nDownload File\n\n\n\n\n\n\n\n\nHolomorphic Poisson Struct
 ures - Lecture 2\nBrent Pym (McGill University)\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n Pym - Holomorphic Poisson Structures - Lecture 2\n\n\n\nDownload File\n
 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nHolomorphic Poisson Structures
  - Lecture 3\nBrent Pym (McGill University)\n\n\n\n\n\n\n\n\n\n\n\n\n\n P
 ym - Holomorphic Poisson Structures - Lecture 3\n\n\n\nDownload File\n\n\n
 \n\n\n\n\n\nHolomorphic Poisson Structures - Lecture 4\nBrent Pym (McGill
  University)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Pym - Holomorphic Poisson Structu
 res - Lecture 4\n\n\n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n\n\n\n\n\nAbstract. The notion of a Poisson manifold originated
  in mathematical physics\, where it is used to describe the equations of m
 otion of classical mechanical systems\, but it is nowadays connected with 
 many different parts of mathematics.  A key feature of any Poisson manifo
 ld is that it carries a canonical foliation by even-dimensional submanifol
 ds\, called its symplectic leaves.  They correspond physically to regions
  in phase space where the motion of a particle is trapped.\n\nI will give 
 an introduction to Poisson manifolds in the context of complex analytic/al
 gebraic geometry\, with a particular focus on the geometry of the associat
 ed foliation.  Starting from basic definitions and constructions\, we wil
 l see many examples\, leading to some discussion of recent progress toward
 s the classification of Poisson brackets on Fano manifolds of small dimens
 ion\, such as projective space.\n\n\n\n\n\n REFERENCES \n\n\n\n\n PROBLEMS
  \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nFANO FOLIATIONS\n\n\n\n\n\n
 \n\n\n\n\n\n\n\n\n\n\n\n\nFano Foliations 0 - Algebraicity of Smooth Forma
 l Schemes and Applications to Foliations\nStéphane Druel (Université Cl
 aude Bernard Lyon 1)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Druel - Algebraicity of S
 mooth Formal Schemes and Applications to Foliations\n\n\n\nDownload File\n
 \n\n\n\n\n\n\n\nFano Foliations 1 -Definition\, Examples and First Propert
 ies  \nCarolina Araujo (IMPA\, Brazil)\n​\n​\n\n\n\n\n\n\n\n\n\n\n\n\
 n\n Araujo - Definition\, Examples and First Properties .pdf\n\n\n\nDownlo
 ad File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nFano Foliations 2 - Adj
 unction Formula and Applications​\nStéphane Druel (Université Claude 
 Bernard Lyon 1)\n​\n\n\n\n\n\n\n\n\n\n\n\n\n\n Druel - Adjunction Formul
 a and Applications\n\n\n\nDownload File\n\n\n\n\n\n\n\n\nFano Foliations 3
  - Classification of Fano Foliations of Large Index\nCarolina Araujo (IMP
 A\, Brazil)​\n\n\n\n\n\n\n\n\n\n\n\n\n\n Araujo - Classification of Fano
  foliations of large index.pdf\n\n\n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\
 n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nAbstract. In the last few decades\, mu
 ch progress has been made in birational algebraic geometry. The general vi
 ewpoint is that complex projective manifolds should be classified accordin
 g to the behavior of their canonical class. As a result of the minimal mod
 el program (MMP)\, every complex projective manifold can be built up from 
 3 classes of (possibly singular) projective varieties\, namely\,  varieti
 es $X$ for which  $K_X$ satisfies $K_X&lt\;0$\, $K_X\\equiv 0$ or $K_X&gt
 \;0$. Projective manifolds $X$ whose anti-canonical class $-K_X$ is ample 
 are called Fano manifolds.\n\nTechniques from the MMP have been successful
 ly applied to the study of global properties of holomorphic foliations. Th
 is led\, for instance\, to Brunella's birational classification of foliati
 ons on surfaces\, in which the canonical class of the foliation plays a ke
 y role. In recent years\, much progress has been made in higher dimensions
 . In particular\, there is a well developed theory of Fano foliations\, i.
 e.\, holomorphic foliations $F$ on complex projective varieties with ample
  anti-canonical class  $-K_F$.\n\nThis mini-course is devoted to reviewin
 g some aspects of the theory of Fano Foliations\, with a special emphasis 
 on Fano foliations of large index. We start by proving a fundamental algeb
 raicity property of Fano foliations\, as an application of Bost's criterio
 n of algebraicity for formal schemes. We then introduce and explore the co
 ncept of log leaves. These tools are then put together to address the prob
 lem of classifying Fano foliations of large index.\n\n\n\n\n\n REFERENCES 
 \n\n\n\n\n PROBLEMS \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nMINIMAL MODEL PROGRA
 M\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nAn Overview of the Minima
 l Model Program - Lecture 1\nPaolo Cascini (Imperial College)\n\n\n\n\n\n
 \n\n\n\n\n\n\n\n Cascini - Minimal Model Program for Foliations.pdf\n\n\n\
 nDownload File\n\n\n\n\n\n\n\n\nMMP for co-rank1 Foliations - Lecture 1\nC
 alum Spicer (King’s College)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Spicer - MMP f
 or co-rank1 foliations.pdf\n\n\n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\n\n\
 n\n\n\n\n\n\n\n\nMMP for co-rank1 Foliations - Lecture 2\nCalum Spicer (K
 ing’s College)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Spicer -MMP for co-rank1 Foli
 ations2.pdf\n\n\n\nDownload File\n\n\n\n\n\n\n\n\nMMP for Foliations of Ra
 nk One Lecture 2\nPaolo Cascini (Imperial College) ​\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n Cascini - MMP for Foliations of Rank One.pdf\n\n\n\nDownload Fi
 le\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nAbstract. The goal
  of the Minimal Model Program (MMP) is to provide a framework in which the
  classification of varieties or foliations can take place. The basic strat
 egy is to use surgery operations to decompose a variety or foliation into 
 "building block" type\nobjects (Fano\, Calabi-Yau\, or canonically polariz
 ed objects).We first review the basic notions of the MMP in the case of va
 rieties.  We then explain work on realizing the MMP for foliations on thr
 eefolds (both in the case of codimension =1 and dimension =1 foliations). 
 We explain and pay special attention to results such as the Cone and Contr
 action theorem\, the Flip theorem and a version of the Basepoint free theo
 rem.\n\n\n\n REFERENCES \n\n\n\n\n PROBLEMS \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n\n\n\nCOMPLETE HOLOMORPHIC VECTOR FIELDS AND THEIR SINGULAR POIN
 TS\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nComplete Holomorphic Vector Fiel
 ds and their Singular Points - Lecture 1\nAdolfo Guillot (UNAM)\n\n\n\n\
 n\n\n\n\n\n\n\n\n\n Guillot-Complete holomorphic vector fields-1.pdf\n\n\n
 \nDownload File\n\n\n\n\n\n\n\n\nComplete Holomorphic Vector Fields and th
 eir Singular Points - Lecture 2\nAdolfo Guillot (UNAM)\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n Guillot-Complete holomorphic vector fields-2.pdf\n\n\n\nDownloa
 d File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nComplete Holomorphic V
 ector Fields and their Singular\nPoints - Lecture 3\nAdolfo Guillot (UNAM
 )\n\n\n\n\n\n\n\n\n\n\n\n\n\n Guillot-Complete holomorphic vector fields-3
 .pdf\n\n\n\nDownload File\n\n\n\n\n\n\n\n\nComplete Holomorphic Vector Fie
 lds and their Singular\nPoints - Lecture 4\nAdolfo Guillot (UNAM)\n\n\n\n
 \n\n\n\n\n\n\n\n\n\n Guillot-Complete holomorphic vector fields-4.pdf\n\n\
 n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nAbst
 ract. On a complex manifold\, complex flows induce complete holomorphic v
 ector fields. However\, only very seldomly a vector field integrates into 
 a flow. In general\, it is difficult to say whether a holomorphic vector f
 ield on a non-compact manifold is complete or not (vector fields on compac
 t manifolds are always complete). Some twenty-five years ago\, Rebelo real
 ized an exploited the fact that there are local (and not just global!) obs
 tructions for a vector field to be complete. This opened the door for a lo
 cal study of complete holomorphic vector fields on complex manifolds. In t
 his series of talks we will explore some of these results.\nWhat I will ta
 lk about is for the greater part contained or summarized in the articles i
 n the bibliography. Their introductions might be useful as a first reading
  on the subject.\n\n\n\n REFERENCES \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nCODI
 MENSION ONE FOLIATIONS WITH PSEUDO-EFFECTIVE CONORMAL BUNDLE\n\n\n\n\n\n\n
 \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nCodimension One Foliations with Pseudo-E
 ffective Conormal Bundle Lecture 1\nFrédéric Touzet (Université Rennes
  1)\n\n\n\n\n\n\n\n\n\n\n\n\n\n Touzet - Part 1 - Codimension one foliatio
 ns with pseudo-effective conormal bundle\n\n\n\nDownload File\n\n\n\n\n\n\
 n\n\nCodimension One Foliations with Pseudo-Effective Conormal Bundle Lect
 ure 2\nFrédéric Touzet (Université Rennes 1)\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n Touzet - Part 2 - Codimension one foliations with pseudo-effective cono
 rmal bundle\n\n\n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \nCodimension one Foliation with Pseudo-Effective Conormal Bundle  Lectur
 e 3\nFrédéric Touzet (Université Rennes 1)\n\n\n\n\n\n\n\n\n\n\n\n\n\n
  Touzet - Part 3 - Codimension one foliations with pseudo-effective conorm
 al bundle\n\n\n\nDownload File\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \n\n\n\n\n\n\nAbstract. Let X be a projective manifold equipped with a co
 dimension 1 (maybe singular) distribution whose conormal sheaf is assumed 
 to be pseudoeffective. Basic examples of such distributions are provided b
 y the kernel of a holomorphic one form\, necessarily closed when the ambie
 nt is projective. More generally\, due to a theorem of Jean-Pierre Demaill
 y\,   a distribution with conormal sheaf pseudoeffective is actually int
 egrable and thus defines a codimension 1 holomorphic foliation F. In this 
 series of lectures\,  we would aim at describing the structure of such a 
 foliation\, especially in the non abundant case\, i.e when F cannot be def
 ined by a  holomorphic one form (even passing through a finite cover).  
 It turns out that \\F is the pull-back of one of the "canonical foliations
 "  on a Hilbert modular variety. This result remains valid for 'logarithm
 ic foliated pairs'.\n\n\n\n REFERENCES \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\
 n\n\n\n\n  \n
CATEGORIES:École ou Master class,Morlet Chair Semester,Virtual event
LOCATION:Luminy - CIRM\, 163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - CIRM:geo:0,0
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