Algebraic K-theory and Chromatic Homotopy Theory - Lecture 2

Explore the second lecture in a four-part series focusing on descent and "soft redshift" in the context of algebraic K-theory and chromatic homotopy theory. Delve into advanced mathematical concepts where linear algebra meets spectra through a homotopy-theoretic lens. Learn how chromatic homotopy theory organizes spectra into periodic families and discover the relationship between algebraic K-theory and cohomological invariants of rings. Examine classical theorems by Thomason, Mitchell, and Hesselholt-Madsen, along with recent developments in Rognes and Ausoni-Rognes' "redshift" conjectures. Understand the implications of these mathematical advances, including their role in disproving the telescope conjecture through the work of Burklund-Hahn-Levy-Schlank. This lecture, presented by Dustin Clausen at the Institut des Hautes Etudes Scientifiques (IHES), forms part of a comprehensive exploration of the intersection between algebraic K-theory and chromatic homotopy theory.