Quadratic forms on rings and the homotopy limit problem

Hermitian K-theory is an invariant of rings (or, more generally, schemes) constructed using the behaviour of quadratic forms. In recent years significant progress has been made in the study of it for rings where 2 is not invertible. In this talk I will give an introduction to the subject from a modern perspective, using as a guide work in progress on the homotopy limit problem, which essentially is asking how much information we can recover from just knowing the algebraic K-theory of the ring.