Quantitative disjointness of nilflows from horospherical flows

TL;DR

This paper establishes a quantitative version of the disjointness between nilflows and horospherical flows, enhancing understanding of their dynamical independence using advanced structural and analytical techniques.

Contribution

It introduces a quantitative disjointness theorem for nilflows and horospherical flows, building on Venkatesh's method and recent structural results by Green, Tao, and Ziegler.

Findings

Proves a quantitative disjointness theorem for nilflows and horospherical flows.

Utilizes a combination of Venkatesh's technique and recent structural theorems.

Advances the understanding of dynamical independence in homogeneous dynamics.

Abstract

We prove a quantitative variant of a disjointness theorem of nilflows from horospherical flows following a technique of Venkatesh, combined with the structural theorems for nilflows by Green, Tao and Ziegler.