English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This mostly expository paper centers on recently proved conjectures in twoareas:  A) A conjecture of A. Oppenheim on the values of real indefinite quadraticforms at integral points.  B) Conjectures of Dani, Raghunathan, and Margulis on closures of orbits inspaces of lattices such as ${\BSL}_n(\R)/{\BSL}_n(\Z)$.  At first sight, A) belongs to analytic number theory and B) belongs toergodic and Lie theory, and they seem to be quite unrelated. They arediscussed together here because of a very interesting connection between thetwo pointed out by M. S. Raghunathan, namely, a special case of B) yields aproof of A).

Values of indefinite quadratic forms at integral points and flows on spaces of lattices