Talk cancelled----Anna Johansson: Hausdorff dimensions in Zaremba theory

The talk is cancelled!

Abstract: The exact value of the Hausdorff dimension of the continued fraction limit set is crucial in Zaremba theory. Several attempts have been made to estimate its Hausdorff dimension, including a very simple and practical method by Pollicott and Vytnova, which uses a combination of min max inequalities, Lagrange-Chebyshev interpolation, and a classic bisection procedure. One interesting question that arises is whether we can generalise these methods to negative (or even more general) continued fractions, in order to formulate conditions on the corresponding limit
sets that could imply results related to Zaremba's conjecture. Some interesting issues arise when looking at negative continued fractions, which could make the topic an interesting problem to study.