Video of the lecture.
Waiting room video: Timothy Gowers talking about the work of John Milnor.

Defined the Euler characteristix χ(X) of a space X to be the Euler characteristic χ(K) of any simplicial complex K with |K| homeomorphic to X. Stated the theorem that is needed to make sure this definition is well-defined.

Gave some triangulations of a circle, torus, Möbius strip, 2-sphere and computed the Euler characteristic of these spaces from the triangulation.

Talked briefly about the Hauptvermutung.