IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

The parametrised Whitehead torsion is an invariant of families of manifolds, and can be viewed as a map to an algebraic K-theory space. A strong version of the nearby Lagrangian conjecture says that when applied to families of closed exact Lagrangians in a cotangent bundle, this invariant vanishes.
Abouzaid and Kragh showed that in this case, this map lands in the trivial path component of the target, i.e. is trivial on $\pi_0$. Using generating functions, we find strong constraints on what this map does to higher homotopy groups. I'll illustrate this with some concrete consequences for the symplectic mapping class group of $T^*T^n$ relative to the 0-section.
This is based on joint work-in-progress with Sylvain Courte.