Besides the student presentations, we are delighted to have the following distinguished speakers to deliver plenary talks at YMC 2019: Moon Duchin (Tufts University), Sam Payne (University of Texas at Austin), and  Tatiana Toro (University of Washington).

The last decade has seen spectacular and continuing advances in an approach to ergodic theory and its applications using the techniques and tools of thermodynamic formalism. The aim of this workshop is to progress this theory by focusing on a number of outstanding problems and challenges. The workshop will also be an opportunity to celebrate the 60th birthday of Mark Pollicott. 

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