Tomer Schlank

A Clay Research Award is made to Robert Burklund (Copenhagen), Jeremy Hahn (MIT), Ishan Levy (IAS and CMI), and Tomer Schlank (Chicago) in recognition of their remarkable construction of counterexamples to Ravenel’s “Telescope Conjecture.”

The Telescope Conjecture was the last open conjecture from Ravenel’s visionary paper “Localization with respect to certain periodic homology theories.”  That paper, and the body of work it inspired, form the bedrock of chromatic homotopy theory.  In one version, the telescope conjecture postulates an upper bound on the growth rate of the chromatic layers of the stable homotopy groups of spheres.  The work of Burklund, Hahn, Levy and Schlank is the crest of a revolutionary new wave in K-theoretic techniques, to which they have each, independently, contributed. Their counterexamples imply that the p-rank of the stable homotopy groups of spheres grows faster than expected, and contains a proliferation of elements that are unaccountable by any prior understanding of the subject.  This is a milestone achievement.