Mark Pollicott (Warwick)
Continued fraction Cantor sets, their Hausdorff dimension and applications
Abstract: We will consider Cantor sets in the real line arising from continued fraction expansions with uniformly bounded digits. Our main results relate to estimates on the Hausdorff dimension of such sets. We will discuss applications to the Zaremba conjecture and the Markoff-Lagrange spectra, in number theory. This is joint work with P. Vytnova.