Luogo: Aula Newton - Plesso FisicoRelatore: David Hilditch - Institute for Theorethical Physics,Friedrich-Schiller-Universität Jena, GermanyE-mail Organizzatore: raffaella.burioni@fis.unipr.itAbstract:Abstract. In my presentation I will give an introduction to numericalrelativity, starting with an elementary discussion of the field equationsof general relativity. I will explain the relevance of PDE theory,numerical analysis and high-performance-computing to the study of extremespacetimes. Afterwards I will discuss progress in the evolution ofgravitational waves that 'just about' collapse to form a black hole. I willexplain why we might expect to see critical phenomena in this regime andits relevance to the cosmic censorship conjecture.