This mini-course is devoted to a set of symmetry-based tricks in a theory of continued fractions that proven themselves to be useful over the years, with the main one being the so-called "Folding lemma". Applications to be discussed include constructing numbers with given irrationality exponent lying in a Cantor set in both real and complex settings, getting diophantine properties of fixed points of Minkowski question mark function, obtaining non-trivial bounds in Zaremba’s conjecture, and even a continued fraction-based proof of Fermat’s theorem on sums of two squares.

Meeting ID: 920 1213 5415 Password: 608175