Localisation in Homotopy Theory by Abhinandan Das

Explore the fundamental concepts of localization in homotopy theory in this comprehensive lecture by Abhinandan Das. Delve into the intricate world of algebraic topology as part of the "Dualities in Topology and Algebra" program organized by the International Centre for Theoretical Sciences. Learn about the connections between algebraic topology, commutative algebra, and modular representation theory of finite groups. Discover how localization techniques are applied in homotopy theory and their significance in understanding duality phenomena and classification problems in tensor-triangulated categories. Gain insights into the derived category of commutative rings, stable categories, and the stable homotopy category in topology. Examine the similarities and differences between these categories, including their triangulated structures and symmetric products. Investigate the application of concepts from commutative algebra and algebraic geometry to modular representation theory and stable homotopy category, such as Grothendieck duality theory and Gorenstein rings. Explore the classification of thick and localizing subcategories of triangulated categories and the computation of their spectra. Enhance your understanding of cohomological support varieties and their development in modular representation theory. This lecture is suitable for those with a background in algebraic topology, commutative algebra, and homological algebra.