Chromatic homotopy theory decomposes stable homotopy theory into an infinite sequence of periodic strata, each of which has the potential to be completely computable. These ideas were made precise by the Ravenel Conjectures, which were famously solved by various combinations of Devinatz, Hopkins, Smith, and Ravenel in the decade which followed, except for one: the Telescope Conjecture. This conjecture eluded resolution until 2023, when it was shown to be false by Burklund-Hahn-Levy-Schlank. The disproof involved the discovery of a new and unexpected interface between algebraic K-theory and chromatic homotopy theory which augmented an existing and growing understanding of relationship between these two subjects as witnessed by the Quillen-Lichtenbaum Conjecture, Thomason's Descent Theorem, and the Rognes Redshift Conjecture.

The aim of this workshop is to address the question "what next?". We aim to explore this question narrowly (what does the failure of the telescope conjecture say about v_n-periodic homotopy groups?) and broadly (what are the next horizons for homotopy theory/algebraic topology/K-theory now that this major problem has been solved?). The goal of the workshop is to bring together researchers in chromatic homotopy theory, algebraic K-theory, and a variety of other neighboring areas to address these questions.

Travel support is available for US based participants thanks to the National Science Foundation.

Application details Deadline for applications: 30 Mar 2025