He has published a number of works on photography, most notably the three-volume series—La photographie—on the history of photography (2000–2010), which belongs to the collection Découvertes Gallimard,[2] as well as Parr by Parr: Discussions with a Promiscuous Photographer (2011), Stephen Shore: Solving Pictures (2017), Being Modern: MoMA in Paris (co-author with Olivier Michelon, 2017).
[2] In 2010, he was appointed Head of the Cabinet de la Photographie at the Musée National d'Art Moderne, and a professor at the École du Louvre.
In January 2013, he was appointed The Joel and Anne Ehrenkranz Chief Curator of Photography at the Museum of Modern Art (MoMA) in New York City.
[2][3] Bajac remained in that post at MoMA until becoming director of the Galerie nationale du Jeu de Paume in Paris in November 2018.
As the chief curator of photography at MoMA, he organised A World of Its Own: Photographic Practices in the Studio (2014), Scenes for a New Heritage: Contemporary Art from the Collection (2015), and Stephen Shore (2018).