David Gabai is the Hughes-Rogers Professor of Mathematics at Princeton University. He arrived in 2001 and served as Chair from 2012 to 2019. Previous to Princeton, he was at California Institute of Technology for 15 years and was an assistant professor at the University of Pennsylvania and a Benjamin Pierce Instructor at Harvard before that. He received his Ph.D. from Princeton University in 1980 with William Thurston as his advisor and was an undergraduate at Massachusetts Institute of Technology.
Gabai’s early research focused on foliations on 3-manifolds, then shifted to the study of hyperbolic 3-manifolds and then to smooth 4-D topology. His seminal work on sutured manifold hierarchies led to a general construction of taut foliations and the resolution of a strong form of the Property R conjecture, which is crucial to many applications of gauge theory and Floer theory. As byproducts, he introduced the notion of thin position, which is now a basic tool in geometric topology and proved the 2-D simple loop conjecture. Together with Oertel, he introduced and developed the foundations of essential laminations. His work on hyperbolic geometry includes proofs of the Smale conjecture for hyperbolic 3-manifolds, the Marden’s tameness and Ahlfors measure conjectures (both with Danny Calegari and independently Ian Agol), the conjecture that the Weeks manifold is the unique minimum volume hyperbolic 3-manifold (with Rob Meyerhoff and Peter Milley) and very recently the Gordon conjecture on non-hyperbolic fillings (with Robert Haraway, Rob Meyerhoff, Nathaniel Thurston and Andrew Yarmola). He proved the 4-dimensional light bulb theorem in smooth 4-dimensional topology.
His research was recognized with the 2004 Veblen Prize and a 2009 Clay Research Award, and invited lectures at the 1990 and 2010 International Congress of Mathematicians. He was elected to the National Academy of Sciences in 2011 and the American Academy of Arts and Sciences in 2014.