A. Fish

activity

20052026

most citedCharacteristic Polynomial Patterns in Difference Sets of Matrices

7 citations · 28 across the 31 of their papers we have counts for

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23 papers · 1 filter

math.DS2022

Glasner property for linear group actions and their products

Kamil Bulinski, Alexander Fish

A theorem of Glasner from 1979 shows that if $Y \subset T = R / Z$ is infinite then for each $ε > 0$ there exists an integer $n$ such that $nY$ is $ε$ -dense…

math.DS2021

Reconstructing a minimal topological dynamical system from a set of return times

Kamil Bulinski, Alexander Fish

We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations this is indee…

math.DS2021

Glasner property for unipotently generated group actions on tori

Kamil Bulinski, Alexander Fish

A theorem of Glasner from 1979 shows that if $A \subset T = R / Z$ is infinite then for each $ε > 0$ there exists an integer $n$ such that $n A$ is $ε$ -dense…

math.DS2021

Quantitative twisted patterns in positive density subsets

Kamil Bulinski, Alexander Fish

We make quantitative improvements to recently obtained results on the structure of the image of a large difference set under certain quadratic forms and other homogeneous polynomia…

math.DS2020

Direct and inverse results for popular differences in trees of positive dimension

Alexander Fish, Leo Jiang, with a joint appendix with Ilya D. Shkredov

We establish analogues for trees of results relating the density of a set $E \subset N$ , the density of its set of popular differences, and the structure of $E$ . To obtain…

math.DS2019

Sets of transfer times with small densities

Michael Björklund, Alexander Fish, Ilya D. Shkredov

We consider in this paper the set of transfer times between two measurable subsets of positive measures in an ergodic probability measure-preserving system of a countable abelian g…