In June 2023, Burklund, Hahn, Levy, and Schlank surprised the homotopy theory community when they announced a disproof of Ravenel's Telescope Conjecture, a fundamental problem of homotopy theory which had been open for 40 years and was believed to be out of reach. The disproof of the Telescope Conjecture combines some of the most exciting recent developments in homotopy theory. This includes fundamental work on red-shift phenomena and descent in algebraic K-theory, trace methods based on a novel approach to topological Hochschild and cyclic homology, ambidexterity in chromatic homotopy theory, and more.

The workshop will explore this amazing body of work, culminating in its synthesis and ingenious application to disprove the Telescope Conjecture.

In recent years techniques from harmonic analysis viz. projection theorems have found striking applications in finitary analysis on homogenous spaces. Such quantitative results have many potential applications to analytic number theory. This workshop will bring together researchers in these areas to further explore these connections.