Talk 3: Motives as a localization of categories

The category of localizing motives is the recipient of the universal localizing invariant, and will be one of the main characters of this conference. I will report on joint work with Vova Sosnilo and Christoph Winges, where we give a new perspective on this category, closer in spirit to the operator theoretic $KK$-category. Namely, we prove that this category is a localization of the category of stable categories. I will discuss a proof of this result as well as applications thereof.