The Family Signature Theorem

Explore a 46-minute lecture on the family signature theorem presented by Oscar Randal-Williams from the University of Cambridge at the Fields Institute. Delve into the extension of Hirzebruch's signature theorem to families of smooth manifolds, examining how it relates the Chern character of a vector bundle constructed from local systems of intersection forms to the fibre integral of the L-class. Learn about the application of the family index theorem for the fibrewise signature operator in this context. This talk was part of the Conference on Homotopy Theory with Applications to Arithmetic and Geometry held from June 27-30, 2022.