Ambidexterity III by Neil Strickland

Explore the concept of ambidexterity in mathematics through this lecture by Neil Strickland, part of the "Dualities in Topology and Algebra" program at the International Centre for Theoretical Sciences. Delve into advanced topics in algebraic topology, commutative algebra, and modular representation theory of finite groups, focusing on duality phenomena and classification problems in tensor-triangulated categories. Gain insights into the connections between derived categories of commutative rings, stable categories of finite groups, and stable homotopy categories in topology. Examine how ideas from commutative algebra and algebraic geometry have been applied to modular representation theory and stable homotopy theory, including Grothendieck duality theory and Gorenstein rings. Discover the classification of thick and localising subcategories of triangulated categories and the computation of their spectra in the sense of Balmer. Suitable for those with a background in algebraic topology, commutative algebra, and homological algebra.