Explore the fascinating world of minimal-volume cusped orientable hyperbolic 3-manifolds in this 33-minute conference talk by Dale Rolfsen from the University of British Columbia. Delve into joint research with Eiko Kin, examining the fundamental groups of one-cusp and two-cusp minimal examples. Discover how some of these groups are bi-orderable while others are not. Learn about the concept of "order-preserving" braids and their connection to the Artin action on the automorphism group of the free group F_n. This talk, part of the Workshop on Orderable Groups at the Centre de recherches mathématiques, offers valuable insights into the intersection of hyperbolic geometry, group theory, and braid theory.