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Explore a lecture series delving into the intersection of algebraic K-theory and chromatic homotopy theory, examining how spectra can be organized into periodic families through chromatic homotopy theory while investigating algebraic K-theory as a cohomological invariant of rings. Learn about foundational theorems from Thomason, Mitchell, and Hesselholt-Madsen, and discover how recent work has proven several of Rognes and Ausoni-Rognes' "redshift" conjectures. Progress through four comprehensive lectures covering introduction to chromatic homotopy theory, descent and "soft redshift," the Lichtenbaum-Quillen property ("hard redshift"), and the telescope conjecture, including its recent resolution by Burklund-Hahn-Levy-Schlank. Master advanced mathematical concepts presented over four sessions at the Institut des Hautes Etudes Scientifiques (IHES), gaining insights into the latest developments in pure chromatic homotopy theory.
