Title: Homological mirror symmetry for projective K3 surfaces

Abstract: Joint work with Ailsa Keating. We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: the Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on its mirror, which is a K3 surface of Picard rank 19 over the field of formal Laurent series. This builds on work of Seidel, Sheridan, Lekili-Ueda, and Ganatra-Pardon-Shende. I will not assume prior knowledge of the Fukaya category.