Number Theory Seminar: p-adic Geometry and Chromatic Homotopy Theory

Chromatic homotopy theory relates the structure of stable homotopy groups to the geometry of formal groups. I will explain how the Faltings–Fargues comparison between the Lubin–Tate and Drinfeld towers, together with recent advances in p-adic Hodge theory, and more recent analogs,  provides tools for addressing longstanding questions in homotopy theory. Applications include the rational homotopy groups of the K(n)-local sphere, Hopkins’ Picard group, and the chromatic splitting conjecture. The talk is based on joint work with Tobias Barthel, Lucas Mann, Rin Ray, Andy Senger, Nathaniel Stapleton, Jared Weinstein, and Xinyu Zhou.