[1] She returned to work at National Museum of Iceland as a curator, but later resigned in protest at the conservative reforms the institution was making.

[2] Ólafía began her doctoral research at the Lund University where she examined Icelandic sagas as historical texts.

[2] Ólafía's research was concerned with the chronology and temporal structure of Icelandic saga literature.

[2] Her research also encompassed the use of Latin by Icelandic writers,[6] the cult of Guðmundr Arason,[7] Archbishop Absalon,[8] and many other subjects, including the role of women.

[3] Ólafía was married to Bent Fuglede, a mathematician, who she met whilst on a trip to Copenhagen, Denmark.