[2] In 2012–13, he was a visiting scholar at the Institute for Advanced Study,[3] where he was one of the official participants in the Special Year on Univalent Foundations of Mathematics.
[4] Shulman was one of the principal authors of the book Homotopy type theory: Univalent foundations of mathematics,[5] an informal exposition on the basics of univalent foundations and homotopy type theory.
[6] In 2014, Shulman was part of a team headed by Steve Awodey that was awarded a $7.5M grant from the Air Force Research Laboratory for homotopy type theory.
[7] Shulman is a supporter of using web-based software systems, such as GitHub, to promote collaborative work by mathematicians—the six-hundred-page Homotopy type theory book being a notable example.
He is a prolific contributor to the nLab[8] (and a member of its steering committee[9]), and a co-host of the homotopy type theory blog[10] and of the n-Category Cafe, a blog focusing on higher category theory.