THE TWENTIETH COLLOQUIUMFEST Speaker: Przemyslaw Koprowski Title: Wild and even points in global fields and beyond Abstract: The talk will concentrate on an intricate interplay between arithmetic, valuations and quadratic forms. We shall concentrate on so called `wild sets' of primes of a global field (the precise definition will be provided during the talk), which are basically the sets where a correspondence between valuations and quadratic forms breaks down. We will report on our ongoing efforts to describe the structure of finite wild sets. This is joint work with Alfred Czogala and Beata Rothkegel.