Alexander Fish

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20242026

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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…

math.DS2024

Michael BjÃ¶rklund, Alexander Fish

An extension of SzemerÃ©di's Theorem is proved for sets of positive density in approximate lattices in general locally compact and second countable abelian groups. As a consequence…

Trace spectra of simplices in large sets

Dynamics of multiplicative groups over fields and Folner-Kloosterman sums

Ehrhart spectra of large subsets of Zr

A SzemerÃ©di type theorem for sets of positive density in approximate lattices

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