Schlank is primarily known for his work on
chromatic homotopy theory. Together with Robert Burklund, Jeremy Hahn, and Ishan Levy, he disproved the
telescope conjecture for all heights greater than 1 and for all primes. This was the last outstanding conjecture among
Ravenel's conjectures. The disproof made use of his work on ambidexterity of the T(n)-local category and cyclotomic extensions of the T(n)-local sphere with Ben-Moshe, Carmeli, and Yanovski. With Barthel, Stapleton, and Weinstein, he calculated the homotopy groups of the rationalization of the K(n)-local sphere. With Burklund and Yuan, Schlank proved the "chromatic nullstellensatz", a version of
Hilbert's nullstellensatz for the T(n)-local category in which Morava E-theories play the role of algebraically closed fields. This work resolved the Ausoni—Rognes
redshift conjecture for E_\infty-ring spectra and also produced E_\infty-orientations of Morava E-theory. Schlank's early work was a synthesis of homotopy theory and number theory. With Harpaz, he developed homotopy obstructions to the existence of rational points on smooth varieties over number fields and related these homotopy obstructions to the
Manin obstruction. He wrote his thesis, titled "Applications of homotopy theory to the study of obstructions to existence of rational points", on this topic. Schlank is known for the breadth of his work and for bringing together seemingly unrelated concepts from different fields to solve problems. In mathematics, he has published papers in algebraic geometry, algebraic topology, category theory, combinatorics, dynamical systems, geometric topology, number theory, and representation theory. == References ==