Organization board: Serge Cantat, Christophe Dupont

Scientific board: Matthew Baker, Eric Bedford, Serge Cantat, Christophe Dupont, Mattias Jonsson

In the last 25 years, the body of research about smooth dynamical systems beyond the uniformly hyperbolic setting has grown substantially and at a rapid pace. Every 2-3 years since 2001, a workshop has been held to disseminate new results, establish connections between researchers, and train new generations of early career mathematicians. Carefully chosen mini-courses and a small number of invited talks allow ample time for informal collaboration. Previous workshops have been held in Evanston, 2001, Buzios, 2003, Chicago, 2006, Beijing, 2009, Luminy, 2011, Bedlewo, 2013, and Olmue, 2015.

This program concerns the recent developments in Complex Analysis and its Applications. Among a very large choice of topics, we will focus on those related to Pluripotential Theory.

The Pluripotential Theory, a branch of Complex Analysis, was founded in the ’50s by Lelong and Oka. It became a very important and powerful tool  with connections with many mathematical theories: Complex Analysis, Complex Differential Geometry, Complex Algebraic Geometry, Dynamics, Foliations and also in Mathematical Physics. The aim of this program is to bring together experts  who are working in these  topics with interest in pluripotential theory. It will give them an opportunity to learn the recent results and to share their new ideas.

Beside informal discussions and seminars, we will organize a week of mini courses (accessible to PhD students, young researchers and non-experts) and also a one week conference. We would like to emphasize the following research directions:

• Complex dynamics in higher dimension;
• Pluripotential techniques in the theory of holomorphic foliations;
• Bergman kernels and its applications;
• Problems from complex geometry, complex analysis (e.g. Kobayashi hyperbolicity, Nevanlinna theory, manifolds with special Kaehler metrics) and other problems from mathematical physics.

• Tien Cuong Dinh (National University of Singapore)
• George Marinescu (University of Cologne)
• Xiaonan Ma (Université Paris Diderot - Paris 7)
• De-Qi Zhang (National University of Singapore)

Courses:

- Bassam Fayad (Institut de Mathématiques de Jussieu & CNRS, Paris)
"Quasi-periodic Birkhoff sums in smooth ergodic theory"

- Marcel Guardia (Universitat Politècnica de Catalunya, Barcelona)
"Oscillatory motions in the three body problem"

- Vadim Kaloshin (University of Maryland and ETH-ITS Zürich)
"Stochastic Arnol’d diffusion"

- Alfonso Sorrentino (Università di Roma “Tor Vergata”)
"Birkhoff Billiards"

ORGANIZERS: M. Guardia, V. Kaloshin and A. Sorrentino.
marcel.guardia@upc.edu
vadim.kaloshin@gmail.com
sorrentino@mat.uniroma2.it