Andrew Blumberg, Stanford

TITLE: Algebraic K-theory, higher homotopy theory of derived categories, and localization

ABSTRACT: In this talk I will provide a gentle overview of the conceptual perspective that algebraic K-theory (and related invariants like topological Hochschild homology and cylic homology) encode the "higher homotopy theory" of the derived category.  I will discuss recent work with Mandell which makes this slogan precise in terms of constructions from abstract homotopy theory (i.e., the Dwyer-Kan simplicial localization), and I will also discuss applications motivated by this perspective to localization theorems for topological Hochschild homology and topological cyclic homology.