Toronto Probability

The directed landscape is the scaling limit of Brownian last passage percolation and is conjectured to be the universal random metric for models in the KPZ universality class. Let G be the union of all the geodesics without their endpoints. Although G has Hausdorff dimension only 4/3, almost surely every finite length path in the directed landscape spends measure 0 time outside G. In this talk, I will go over techniques used to prove this result. Joint work with Balint Virag and Sourav Sarkar.