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Home » ANT Postdoc Seminar: Job Talk: Bohr sets and multiplicative diophantine approximation

Seminar

ANT Postdoc Seminar: Job Talk: Bohr sets and multiplicative diophantine approximation February 17, 2017 (11:00 AM PST - 11:50 AM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Sam Chow (University of York)
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In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fiber version of Gallagher’s theorem, establishing unconditionally a result recently obtained conditionally by Beresnevich, Haynes and Velani. The idea is to find large generalised arithmetic progressions within inhomogeneous Bohr sets, extending a construction given by Tao. This precise structure enables us to verify the hypotheses of the Duffin–Schaeffer theorem for the problem at hand, via the geometry of numbers.

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