Number theoretic techniques in the theory of Lie groups and differential geometry

Details Number theoretic techniques in the theory of Lie groups and differential geometry Number theoretic techniques in the theory of Lie groups and differential geometry

2008-09-15

arxiv.org/abs/0809.2401v1

Mathematics

Differential Geometry

This is a slightly revised version of a survey article published in the Proceedings of the International Congress of Chinese M

Scientific paper

The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense subgroups in a semi-simple Lie group. We have shown that for arithmetic subgroups, weak commensurability has surprisingly strong consequences. Our proofs make use of p-adic techniques and results from algebraic and transcendental number theory.

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