CARMA OANT SEMINAR Speaker: Dr Dzmitry Badziahin, Department of Mathematical Sciences, Durham University Title: On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: SeeVogh (non-AG) [ENQUIRIES] Time and Date: 10:00 am, Wed, 5th Nov 2014 SeeVogh meeting number 9743677479. Abstract: Mixed Littlewood conjecture proposed by de Mathan and Teulie in 2004 states that for every real number $x$ one has $\liminf q * |q|_D * ||qx|| = 0,$ where $|q|_D$ is a so called pseudo norm which generalises the standard p-adic norm. In the talk we'll consider the set mad of potential counterexamples to this conjecture. Thanks to the results of Einsiedler and Kleinbock we already know that the Haudorff dimension of mad is zero, so this set is very tiny. During the talk we'll see that the continued fraction expansion of every element in mad should satisfy some quite restrictive conditions. As one of them we'll see that for these expansions, considered as infinite words, the complexity function can neither grow too fast nor too slow. [Permanent link]