Complex Geometry, Analysis and Foliations

Talks

24. Marco Brunella and the curvature of canonical line bundles

Jean-Pierre DEMAILLY (Grenoble)

29/09/2014 10:00

The talk will present some striking results of Marco Brunella concerning the curvature of canonical and anticanonical line bundles of compact Kähler manifolds, and of foliations on such manifolds. These results all contain very deep ideas, and several ones are connected to important unsolved conjectures. We will try to give an overview of some of them.

10. Index theorems and geodesic flow for meromorphic connections along foliations

Marco ABATE (Pisa)

29/09/2014 11:30

The study of meromorphic connections on Riemann surfaces is a classical topic, related for instance to the 21st Hilbert problem. In this talk I shall introduce a novel point of view, with unexpected analytic, geometric and dynamical applications. More precisely, I shall show how to associate to holomorphic maps having a positive-dimensional fixed point set a foliation in Riemann surfaces with...

6. Taxonomy of Class VII Surfaces

Matei TOMA (Nancy)

29/09/2014 14:00

In Kodaira's classification of compact complex surfaces Class VII hasn't been yet completely understood. An important part of Marco Brunella's mathematical work deals with dynamical properties of class VII surfaces. Part of this work was published posthumously. In this talk we present new ways of subclassifying class VII surfaces, in which Marco's ideas and results play an important role. We...

5. Holomorphic foliations and invariant currents.

Frédéric TOUZET (Rennes)

29/09/2014 15:30

In this talk, we will point out some numerical properties of codimension 1 foliations on projective manifolds which ensure the existence/inexistence of  holonomy invariant positive current.

14. On deformations of elliptic fibrations, according to Cayley, Cremona, Halphen and Brunella.

Luis Gustavo MENDES (Porto Alegre)

29/09/2014 17:00

In the first part of the talk I'll take the risk of doing history of mathematics, presenting results of Cayley, Cremona and Halphen on deformations of elliptic fibrations (without sections). After, I'll show some experiments of degenerations of the configurations treated by these authors. At last, I'll give some ideas of Brunella's general result on deformations of...

20. Points singuliers de feuilletages holomorphes en dimension 3.

Dominique CERVEAU (Rennes)

30/09/2014 10:00

IL s'agit d'un travail avec Alcides Lins neto et Marianna Vago où l'on donne une description des types de singularités modulo la connaissance de leur partie initiale.

17. Circle actions on the 7-sphere with unbounded periods and non-linearizable multicentres

Massimo VILLARINI (Modena)

30/09/2014 11:30

We give an example of a free circle action on the 7-dimensional sphere whose orbits have unbounded lenghts (equivalently: unbounded periods).As an application we construct a smooth vector field X in a neighbourhood U of the origin in the 8-dimensional real space such that : U - (0) is foliated by closed integrale curves, the differential DX(0) generate a 1-parametri group of rotations, but X...

28. From umbilical foliations to the plurisubharmonic variation of the Poincaré metric

Jorge Vitorio PEREIRA (IMPA)

30/09/2014 14:00

23. From character varieties to isoperiodic foliations: a transfer principle

Bertrand DEROIN (Paris)

30/09/2014 15:30

Schiffer variations are surgery operations that takes an abelian differential on a curve to another one with the same periods. Viewed in the moduli space of abelian differentials of a fixed genus g>=2, they draw a complex algebraic foliation of dimension 2g-3, called the isoperiodic foliation. Its transverse structure is modelled on an open set contained in the group of complex periods, on...

12. A generalization of Malmquist's theorem

Adolfo GUILLOT (Cuernavaca)

30/09/2014 17:00

The centennial theorem of Malmquist states that a non-autonomous algebraic ordinary differential equation of the first order having an entire solution is in fact a Riccati equation. We will speak about related results concerning algebraic differential equations having at least one single-valued solution.

21. Brunella's Local Alternative

Marianna RAVARA VAGO (Rennes)

01/10/2014 09:20

It is a local version of a conjecture of Brunella which says that a codimension 1 foliation in the projective three-dimensional space P^3 either has an invariant algebraic surface or each leaf is sub-foliated by a one-dimensional foliation. In this local take, we have the following "local conjecture": a germ of holomorphic codimension 1 foliation in C^3,0 either possesses a germ of analytic...

19. Kähler threefolds without subvarieties

Misha VERBITSKY (Moscow)

01/10/2014 10:00

Let $M$ be a compact Kahler manifold without non-trivial complex subvarieties. Using Brunella's alternative for holomorphic foliations, Nadel's vanishing theorem and Demailly's regularization of positive currents, we prove that $M$ is a compact torus. This is a joint work with F. Campana and J.-P. Demailly.

9. Foliations with a compact leaf

Frank LORAY (Rennes)

01/10/2014 11:30

We investigate foliations on projective surfaces having a compact leaf. This is a joint work in progress with Benoît Claudon, Jorge Vitorio Pereira and Frédéric Touzet.

18. On periodic orbits in complex billiards

Alexey GLUTSYUK (Lyon and Moscow)

01/10/2014 14:00

A conjecture of Victor Ivrii (1980) says that in every billiard with smooth boundary the set of periodic orbits has measure zero. This conjecture is closely related to  spectral theory. Its particular case  for triangular orbits was proved  by M. Rychlik (1989),  Ya. Vorobets (1994) and other mathematicians, and for quadrilateral orbits in our joint work with Yu. Kudryashov (2012).  We...

22. Complete vector fields on affine surfaces

Matthias LEUENBERGER (Bern)

02/10/2014 09:20

see joint pdf.

26. Marco and the theory of Anosov flows in dimension 3

Etienne GHYS (Lyon)

02/10/2014 10:00

At the beginning of his career, Marco Brunella published five papers related to Anosov flows in dimension 3. These papers had a great influence on the subsequent development of the theory. I would like to review these papers and present the present status of the question.

13. Foliations and webs inducing Galois coverings

Marcel NICOLAU (Barcelona)

02/10/2014 11:30

Motivated by previous work of Cerveau and Déserti, we introduce the notion of Galois holomorphic foliation on the complex projective space as those whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. We characterize Galois foliations on ${\mathbb{P}}^2$ belonging to certain classes, which include homogeneous foliations and we give a geometric...

25. The bi-disc theorem

Michael McQUILLAN (Roma)

02/10/2014 14:00

The identification of surfaces with negative Kodaira dimension which are not fibred in rational curves with the natural foliations on bi-disc quotients can reasonably be considered the centre piece of the classification of foliated surfaces. It was very much a collaborative effort with Marco, and, curiously, I have never given a talk specifically devoted to this theorem.

27. On cohomological invariants of complex manifolds

Adriano TOMASSINI (Parma)

02/10/2014 15:30

We will focus on algebraic aspects of the ${\delta }_1{\delta }_2$-Lemma for bounded double complexes, characterizing it in terms of special cohomologies. We will apply such a result to complex and symplectic manifolds. We will also report on some results on Dolbeault-Massey triple products.

16. Germs of singular holomorphic two dimensional foliations

Alcides LINS NETO (Rio de Janeiro)

02/10/2014 17:00

see joint pdf.

30. Smooth foliations on compact homogeneous kähler varieties

Federico LO BIANCO (Rennes)

03/10/2014 09:20

see joint pdf.

15. The Green-Griffiths locus of quotients of bounded symmetric domains

Simone DIVERIO (Paris)

03/10/2014 10:00

The Green-Griffiths locus is a closed subset of a compact projective manifold which contains the image of all entire curves contained in the manifold. In this talk we shall describe this locus for compact quotients of bounded symmetric domains. It turns out that the following dichotomy holds : either the uniformizing bounded symmetric domain is the ball and the Green-Griffiths locus is empty,...

11. On bihermitian structures on Kato surfaces

Akira FUJIKI (Osaka)

03/10/2014 11:30

There has been much works recently on bihermitian structures on compact complex surfaces, especially in the Kähler case in relation with generalized Kähler geometry. On the other hand , for non-Kähler surfaces we have so far still rather few examples. Recently, however, Apostolov, Bailey and Dloussky have obtained a new nice sufficient condition for their existence. In this talk I will explain...