In the past ten years, there has been a flourishing of new techniques and methods in between foliation theory, birational geometry and local dynamics. This includes the theory of MMP for foliations, which provides a new way to study local and global classical problems in foliation theory. Moreover, the development of methods of resolution of singularities of varieties via weighted blowings-up, some of which inspired by resolution of singularities of vector-fields, are important new tools in birational geometry. It is natural to explore how these methods would impact the study of resolution of singularities of foliations, a problem which is widely open in dimensions higher than 3. Finally, the duality between (formal) vector-fields and local dynamics provides a natural framework to explore complex dynamical systems. The Conference will explore these three inter-connected topics. We will bring together specialists of these three areas of expertise, in order to foster new collaborations and exchanges.

MINI-COURSES Dan Abramovich (Brown University) Resolution of singularities for the dynamical mathematician Lorena López Hernanz (Université de la Alcala) Local dynamics of tangent to the identity biholomorphisms in dimension two Calum Spicer (King’s College London) An introduction to the Minimal Model Program for foliations