Alexander Fish

collaborators

4 papers

math.GR2026

Directional expansion in ergodic actions of countable groups

Michael BjÃ¶rklund, Alexander Fish

We study directional expansion for probability-measure-preserving actions of countable groups through a representation-theoretic group property, the cyclic escape property. An infi…

math.DS2026

Trace spectra of simplices in large sets

Michael BjÃ¶rklund, Alexander Fish, Shrey Sanadhya

Given an ordered tuple $v = (v_{0}, \dots, v_{d})$ of vectors in $R^{d}$ , let $A_{v} = [v_{1} - v_{0} \dots v_{d} - v_{0}]$ be its edge matrix. We prove that, in every fin…

math.DS2025

Dynamics of multiplicative groups over fields and Folner-Kloosterman sums

Michael BjÃ¶rklund, Alexander Fish

For two countably infinite fields whose multiplicative groups are isomorphic, we examine invariant couplings between the actions that these groups induce on the additive Pontryagin…

math.DS2025

Ehrhart spectra of large subsets of $Z^{r}$

Michael BjÃ¶rklund, Rickard Cullman, Alexander Fish

This paper introduces and studies the Ehrhart spectrum of a set $E \subseteq Z^{r}$ , defined as the set of all Ehrhart polynomials of simplices with vertices in $E$ , general…

Directional expansion in ergodic actions of countable groups

Trace spectra of simplices in large sets

Dynamics of multiplicative groups over fields and Folner-Kloosterman sums

Ehrhart spectra of large subsets of Zr

Ehrhart spectra of large subsets of $Z^{r}$