Arbeitsgemeinschaft: Algebraic $K$-Theory and the Telescope Conjecture

The telescope conjecture, first formulated by Ravenel in the late 1970s, is a conjectural classification of smashing localizations of the stable homotopy category. Participants discussed interactions between such localizations and algebraic K -theory, culminating in the recent disproof of the telescope conjecture. We ended with some applications and future directions, including to such classical questions as the growth rate of the stable homotopy groups of spheres.