Algebraic K-theory and Chromatic Homotopy Theory - Lecture 1

Explore a four-part lecture series delving into the intersection of algebraic K-theory and chromatic homotopy theory, beginning with an introduction to chromatic homotopy theory. Learn how spectra serve as the most universal form of linear algebra, and discover how chromatic homotopy theory organizes these spectra into periodic families. Examine the relationship between algebraic K-theory, a sophisticated cohomological invariant of rings, and chromatic theory through classical theorems by Thomason, Mitchell, and Hesselholt-Madsen. Study the "redshift" conjectures proposed by Rognes and Ausoni-Rognes, including recent theoretical developments and their significant impact on chromatic homotopy theory, particularly the resolution of Ravenel's telescope conjecture by Burklund-Hahn-Levy-Schlank. Progress through topics including descent and soft redshift, the Lichtenbaum-Quillen property (hard redshift), and conclude with an examination of the telescope conjecture.