Explore the concept of left-orderability in toroidal 3-manifolds through this 57-minute lecture by Cameron Gordon from the University of Texas at Austin. Delve into the notion of order-detection of slopes for 3-manifolds with torus boundary, as introduced by Boyer and Clay. Examine results on the left-orderability of fundamental groups in 3-manifolds containing incompressible tori. Discover new evidence supporting the L-space conjecture, presented as part of joint work with Steve Boyer and Ying Hu. This talk, delivered at the Workshop on Orderable Groups organized by the Centre de recherches mathématiques (CRM), offers valuable insights for researchers and students in topology and group theory.