Metric techniques for triangulated categories

Neeman has introduced the notion of metrics and approximable triangulated categories. These ideas have been used by Neeman and others to prove a remarkable array of results. In this talk we will discuss some of these results, and their implications in the setting of algebraic geometry. In particular, we discuss a result on passing between (left/right) admissible subcategories of the various essentially small subcategories associated to a variety.