18 citations · 26 across the 3 of their papers we have counts for
9 papers
Almost commuting matrices with respect to the rank metric
Gábor Elek, Łukasz Grabowski
We show that if A_1, A_2, ... , A_n are square matrices, each of them is either unitary or self-adjoint, and they almost commute with respect to the rank metric, then one can find…
Measurable equidecompositions for group actions with an expansion property
Łukasz Grabowski, András Máthé, Oleg Pikhurko
Given an action of a group on a measure space , we provide a sufficient criterion under which two sets are measurably equidecomposable, i.e., can be pa…
Measurable circle squaring
Łukasz Grabowski, András Máthé, Oleg Pikhurko
Laczkovich proved that if bounded subsets and of have the same non-zero Lebesgue measure and the box dimension of the boundary of each set is less than , then ther…
On computing homology gradients over finite fields
Łukasz Grabowski, Thomas Schick
Recently the so-called Atiyah conjecture about l^2-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a m…
Group ring elements with large spectral density
Łukasz Grabowski
Given an arbitrary d>0 we construct a group G and a group ring element S in Z[G] such that the spectral measure mu of S has the property that mu((0,eps)) > C/|log(eps)|^(1+d) for s…
Measurable equidecompositions via combinatorics and group theory
Łukasz Grabowski, András Máthé, Oleg Pikhurko
We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in , for , with non-empty interiors and of the same measure are equidecomposabl…