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This lecture from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar features Noah Porcelli from Imperial College London discussing parametrised Whitehead torsion in the context of families of nearby Lagrangians. Explore how this invariant of families of manifolds maps to algebraic K-theory space, with particular focus on the nearby Lagrangian conjecture for closed exact Lagrangians in cotangent bundles. Learn about Abouzaid and Kragh's demonstration that this map lands in the trivial path component of the target, and discover new constraints on higher homotopy groups using generating functions. The talk includes concrete applications to the symplectic mapping class group of T∗Tn relative to the 0-section, based on joint work-in-progress with Sylvain Courte. This advanced mathematics lecture is scheduled for March 21, 2025.
