Dynamical Systems and Analysis Seminar - Faustin Adiceam
| Dates: | 22 April 2024 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Faustin Adiceam (Université Paris-Est Créteil)
Title: Badly approximable vectors and putative counterexamples to the Littlewood conjecture
Abstract: Answering a question raised by Bugeaud, the talk will be concerned with the determination of the Hausdorff dimension of a natural set interpolating between the set of badly approximable vectors (which is known to have full dimension) and the set of putative counterexamples to the Littlewood conjecture (which is known to have zero Hausdorff dimension). This is obtained by the construction of a so- called generalised Cantor set based on the Ostrowski numeration system induced by a badly approximable number.
Time permitting, a quantitative refinement of this result will be shown to provide an alternative to the multiplicative theory of badly approximable vectors (of which the Littlewood conjecture is a particular case).
This is work in progress with S. Seuret (UPEC).
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
