Approximate Lattices in Higher-Rank Semi-Simple Groups

TL;DR

This paper proves that strong approximate lattices in higher-rank semi-simple algebraic groups are necessarily arithmetic, establishing a significant link between approximate lattice structures and classical arithmetic properties.

Contribution

It demonstrates that all strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic, a novel result connecting approximate and classical lattice theory.

Findings

Strong approximate lattices are arithmetic in higher-rank groups

The result bridges approximate lattice theory with classical arithmetic group theory

Provides new insights into the structure of approximate lattices in semi-simple groups

Abstract

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.