## Period mappings for anti-canonical pairs, by Phillip Griffiths

Anti-canonical pairs (Y, D) are logarithmic K3 surfaces. It is well known that they have a rich geometry. A recent result, whose proof was motivated by mirror-symmetry, establishes a conjecture by Looijenga giving conditions for smoothability of the cusp obtained by contracting D. A central ingredient in the proof is a global Torelli theorem using the mixed Hodge structure on H2(Y −D). In this talk we will formulate and sketch the proof of this result.