Automorphic Forms and Dirac Operators on Conformally Flat Manifolds

TL;DR

This paper explores the relationship between Dirac operators on conformally flat manifolds and automorphic forms, highlighting theoretical connections and applications to boundary value problems.

Contribution

It provides a comprehensive overview of the link between Dirac operators and automorphic forms on conformally flat manifolds, based on fifteen years of collaborative research.

Findings

Established theoretical connection between Dirac operators and automorphic forms.

Outlined applications to boundary value problems.

Summarized fifteen years of joint research work.

Abstract

In this paper we present a summarizing description of the connection between Dirac operators on conformally flat manifolds and automorphic forms based on a series of joint work with John Ryan over the last fifteen years. We also outline applications to boundary value problems.