Complex-analytic methods have revolutionized the study of low-dimensional dynamics during the last several decades. A beautiful synthesis of techniques has emerged, creating a new field which has combined such seemingly disjoint topics such as  the structure of the Mandelbrot set, the stochastic properties of a typical interval map, Feigenbaum-Coullet-Tresser universality and renormalization, among many others. Misha Lyubich’s work has been central to the development of this field, and his 60^th birthday gives us an opportunity to    take stock of the current state of the art, as well as to chart new directions. The aim of the conference is to bring together experts working in the area of complex and real low-dimensional dynamics, and closely related fields of conformal geometry, groups and foliations and general smooth dynamical systems. This wide range of topics is tied together by the general theme of the use of complex methods in dynamics.

Teichmüller theory and moduli spaces of Riemann surfaces have a special role in modern mathematics: they have been a fruitful playground for ideas and methods from complex and algebraic geometry, topology, analysis, and more recently dynamical systems. The main goal of this graduate school is to give the students the opportunity to learn about the various geometric structures on Riemann surfaces and their moduli, and related concepts in Teichmüller theory

The core of the school will be four mini-courses given by

Richard Canary (University of Michigan)
Carlos Matheus (CNRS- Ecole Polytechnique)
Yair Minsky (Yale University)
Scott Wolpert (University of Maryland)

Organized by: Samuel Grushevsky, Babak Modami, and Leon Takhtajan

This year's edition will be special in that it will coincide with the final conference for the Marie Sklodowska Curie Project (IF) 'Combinatorics in transcendental dynamics’. For this reason, we would like to bring together (experienced and junior) researchers in holomorphic dynamics from several different perspectives.  There will be  four minicourses  given by  Misha Lyubich, Han Peters, Lasse Rempe-Gillen, and  Pascale Roesch. Additionally there will be lectures and contributed short talks.

Participants who wish to give a short talk are welcome to submit a title and abstract, and we will do our best to give everyone a chance to speak.

The conference Contemporary mathematics marks the 80^th birthday of Vladimir Arnold  (1937-2010). The Conference will take place in December 18-23, 2017 in Moscow, Russia. The Conference will cover such subjects as Singularity theory, Topology, Differential equations and Dynamical systems, Mathematical Physics, Representation theory, Algebraic geometry, which fall into the domain of interest of Vladimir Arnold. There will be around 20 plenary speakers and around 40 sectional speakers. Financial support for invited speakers and young participants is expected.