Introduction to Chromatic Homotopy Theory - Lecture 2

Delve into the second lecture of the "Introduction to Chromatic Homotopy Theory" series, delivered by Constanze Roitzheim as part of the "Dualities in Topology and Algebra" program. Explore advanced concepts in algebraic topology, focusing on chromatic homotopy theory and its connections to commutative algebra and modular representation theory. Gain insights into duality phenomena and classification problems in tensor-triangulated categories. Examine the relationships between derived categories of commutative rings, stable categories of finite groups, and the stable homotopy category in topology. Discover how ideas from commutative algebra and algebraic geometry have been adapted to enrich modular representation theory and stable homotopy theory. Learn about Grothendieck duality theory, Gorenstein rings and schemes, and their generalizations of classical Poincaré duality for manifolds. Investigate the classification of thick and localising subcategories of triangulated categories, Balmer spectra computation, and cohomological support varieties. Enhance your understanding of algebraic topology, commutative algebra, and homological algebra through this comprehensive lecture series.