Speaker: Demi Allen (University of Bristol, UK)
Title: Dyadic approximation in the middle-third Cantor set
Speaker's URL: https://research-information.bris.ac.uk/en/persons/demi-d-allen
Abstract: Motivated by a classical question due to Mahler, in 2007 Levesley, Salp, and Velani showed that the Hausdorff measure of the set of points in the middle-third Cantor set which can be approximated by triadic rationals (that is, rationals which have denominators which are powers of 3) at a given rate of approximation satisfies a zero-full dichotomy. More precisely, the Hausdorff measure of the set in question is either zero or full according to, respectively, the convergence or divergence of a certain sum which is dependent on the specified rate of approximation. Naturally, one might also wonder what can be said about dyadic approximation in the middle-third Cantor set. That is, how well can we approximate points in the middle-third Cantor set by rationals which have denominators which are powers of 2? In this talk I will discuss a conjecture on this topic due to Velani, some progress towards this conjecture, and why dyadic approximation is harder than triadic approximation in the middle-third Cantor set. This talk will be based on joint work with Sam Chow (Warwick) and Han Yu (Cambridge).
Meeting ID: 955 3124 0801