The theory of holomorphic foliations played an important role in major advances in complex algebraic geometry in the last few decades. It was key to the proof of the abundance conjecture in dimension three and to the 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 foliations with mild singularities is ripe to be developed.
This conference will put together specialists in foliation theory and complex algebraic geometry. It aims at fostering new collaborations at the intersections of these fields, and at disseminating among young researchers the main questions in these fascinating fields of research.
This event is part of a series of activities focusing on Foliation Theory and Complex Geometry, taking place remotely (virtually) as well as residentially at CIRM-Luminy during 2020.