Stratification and Duality for Representations of Finite Groups - Lecture 4

Explore the fourth lecture in a series on stratification and duality for representations of finite groups, delivered by Henning Krause at the International Centre for Theoretical Sciences. Delve into advanced concepts in algebraic topology, commutative algebra, and modular representation theory of finite groups as part of the "Dualities in Topology and Algebra" program. Gain insights into duality phenomena and classification problems in tensor-triangulated categories, examining connections between derived categories of commutative rings, stable categories of finite groups, and stable homotopy categories in topology. Investigate Grothendieck duality theory, Gorenstein rings and schemes, and their applications to generalizing Poincaré duality for manifolds. Learn about the classification of thick and localising subcategories in triangulated categories, Balmer spectra computation, and cohomological support varieties. Enhance your understanding of these complex mathematical concepts through this comprehensive 1 hour and 53 minutes lecture, suitable for those with a background in algebraic topology, commutative algebra, and homological algebra.