This school is a part of the Simons Semester Continued Fractions, Fractals, Ergodic theory and Dynamics. During the school, specialists working in the areas where continued fractions play the key role, such as Diophantine approximation, holomorphic dynamics, ergodic theory, fractal geometry, will introduce both basic concepts and more advanced techniques and results in these areas to younger researchers.

Initially, continued fractions appeared in the 16th century in the work of Italian mathematicians Bombelli and Cataldi as a tool for obtaining best rational approximations of irrational numbers. Now they appear naturally in many areas of mathematics, including: real and complex analysis (Brjuno functions, Pade approximants), holomorphic dynamics (in the study of local behaviour), hyperbolic geometry (characterising metrics on surfaces), KAM theory (studying invariant curves), number theory (when studying Diophantine approximations). In theoretical Computer Science, the study of algorithms related to multidimensional continued fractions and, in particular, convergence rate, is a topic of active research.

Minicourses lecturers:

•  Amir Algom

• Raphael Krikorian

• Nikolay Moshchevitin 

• Kate Stange (tentative)

• Giulio Tiozzo