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Department of Mathematical Sciences

Seminar details

Arithmetic Study Group: A mass transference principle for systems of linear forms with applications to Diophantine approximation

Presented by Demi Allen, University of Manchester

15 May 2018 13:00 in CM219

In Diophantine approximation we are often interested in the Lebesgue and Hausdorff measures of certain
lim sup sets. In 2006, Beresnevich and Velani proved a remarkable result — the Mass Transference Principle —

which allows for the transference of Lebesgue measure theoretic statements to Hausdorff measure theoretic state-
ments for lim sup sets arising from sequences of balls in R

. Subsequently, they extended this Mass Transference

Principle to the more general situation in which the lim sup sets arise from sequences of neighbourhoods of “ap-
proximating” planes. In this talk I will discuss a recent strengthening (joint with V. Beresnevich) of this latter

result in which some potentially restrictive conditions have been removed from the original statement. This
improvement gives rise to some very general statements which allow for the immediate transference of Lebesgue
measure Khintchine–Groshev type statements to their Hausdorff measure analogues and, consequently, has some
interesting applications in Diophantine approximation.

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