Localization techniques are essential to modern mathematics. In commutative algebra and algebraic geometry, localization of rings lets one "zoom-in" on a problem to a particular place, and in nice situations one can assemble all these simpler zoomed-in problems to answer the original one. This idea of "zooming-in" or "inverting irrelevant information is extremely powerful, and its categorical generalizations lead to deep understandings of global structures. In this talk, I will introduce the notion of localization from ring theory and then move on to its categorical analogue, giving examples along the way. I will end with a case-study of brief overview of the telescope conjecture, a long and fabled story about the difference between two particular families of localizations.
Zoom Link: https://washington.zoom.us/j/92849568892