The theory of holomorphic foliations played an important role in major advances in complex algebraic geometry in the last few decades. By means of Miyaoka's generic semi-positivity theorem, it was key to the proof of the abundance conjecture in dimension three. More recently, it was the protagonist in McQuillan's proof of Green-Griffiths conjecture for surfaces of positive Segre class. Foliations also appear naturally on the structure theory of varieties (with mild singularities) with numerically trivial canonical divisor.
Complex algebraic geometry, specially birational geometry, provided a new impetus to the study of foliations and also a new paradigm. There is today a quite satisfactory classification of foliated surfaces according to their Kodaira dimension. Recently, foundational results on numerical properties of the
canonical bundle of foliations have been proved, as well as reduction of singularities for foliations on 3-folds (both in codimension one and in dimension one). These two results together give strong evidence that a birational theory of foliation with mild singularities is ripe to be developed.
This conference will put together specialists in foliation theory, birational geometry, and Kobayashi hyperbolicity. It will certainly foster new collaborations at the intersections of these fields, and will disseminate among young researchers the main questions in these fascinating fields of research.
The conference will aim to cover the following topics:
• Birational geometry of foliations
• Reduction of singularities of foliations
• Structure of Fano and Calabi-Yau foliations
• Entire curves and jet differentials
• Criteria for the existence of algebraic leaves.
INVITED SPEAKERS (tbc)