Arithmetic Geometry and Analysis on Foliated Spaces

TL;DR

This paper introduces the interplay between arithmetic geometry and analysis on foliated spaces, exploring conjectural links between number theory and dynamical systems, aimed at providing an accessible overview for researchers.

Contribution

It offers a streamlined, updated introduction to conjectural relations connecting number theory and dynamical systems on foliated spaces.

Findings

Preliminary insights into the relations between number theory and foliated dynamical systems

Updated overview of existing conjectures and theoretical frameworks

Potential pathways for future research in arithmetic geometry and foliations

Abstract

This report on the topics in the title was written for a lecture series at the Southwestern Center for Arithmetic Algebraic Geometry at the University of Arizona.It may serve as an introduction to certain conjectural relations between number theory and the theory of dynamical systems on foliated spaces. The material is based on streamlined and updated versions of earlier papers on this subject.