Graduate School on Chromatic Homotopy Theory - Part 1

Explore the foundational concepts of chromatic homotopy theory in this graduate-level lecture delivered by Agnès Beaudry from the University of Colorado Boulder at the Fields Institute. Delve into the sophisticated mathematical framework that organizes stable homotopy theory through chromatic filtrations and periodic phenomena. Learn how chromatic homotopy theory provides a systematic approach to understanding the stable homotopy groups of spheres and other fundamental objects in algebraic topology. Examine the role of formal group laws, complex cobordism, and the chromatic spectral sequence in this theoretical landscape. Discover how this field connects algebraic topology with algebraic geometry and number theory through the study of Morava K-theories and Lubin-Tate spectra. Gain insight into the chromatic resolution of the sphere spectrum and its implications for computational methods in stable homotopy theory. This lecture serves as the opening session of a comprehensive graduate school program designed to provide advanced students and researchers with the tools needed to work in this active area of modern algebraic topology.