Arithmetic Groups of Higher Real Rank Are Not Left-orderable

Explore a 53-minute conference talk on the non-left-orderability of arithmetic groups with higher real rank. Delve into the intricate world of Zariski dense subgroups, number theory, and geometric applications as presented by Dave Morris at the International Centre for Theoretical Sciences. Gain insights into recent advancements in the theory of arithmetic and Zariski-dense subgroups, their applications in algebraic and differential geometry, combinatorics, and other fields. Discover the use of algebraic and analytic number theory techniques in solving long-standing problems such as fake projective planes, isospectral and length-commensurable locally symmetric spaces, and expanding graphs. Learn about new approaches to Bruhat-Tits theory, groups with good reduction, and the concept of eigenvalue rigidity in isospectral locally symmetric spaces. Understand how these ideas can potentially be applied to pseudo-Riemannian geometry and the classification of compact space forms.