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Learn about isovariant homotopy theory in this comprehensive 2-hour lecture delivered by Inbar Klang from Vrije Universiteit Amsterdam at the Fields Institute. Explore the fundamental concepts and advanced techniques in this specialized area of algebraic topology that deals with equivariant homotopy theory where the group action is allowed to vary. Delve into the theoretical framework that extends classical homotopy theory to incorporate group actions in a flexible manner, examining how isovariant methods provide powerful tools for understanding spaces with varying symmetries. Discover the applications and connections to broader areas of algebraic topology and homotopy theory through detailed mathematical exposition and rigorous analysis of key results in this emerging field.