After receiving his Ph.D from SUNY at Stony Brook in 1991
under the direction of Ronald G.
Douglas, Yu spent time at the Mathematical Sciences Research Institute (1991-1992), the University of Colorado at Boulder (1992-2000), Vanderbilt University (2000-2012), and a variety of visiting positions.
He currently holds the Powell Chair in Mathematics
and was appointed University Distinguished Professor in 2018 at Texas A&M University.
He is a fellow of the American Mathematical Society.Yu's research interests include noncommutative geometry, higher index theory of elliptic operators, K-theory, and geometric group theory.
He is best known for his fundamental contributions to the Novikov conjecture on homotopy invariants of higher signatures, the Baum-Connes conjecture on K-theory of group C*-algebras, and the stable Borel conjecture on rigidity of manifolds.
In his work on the Novikov conjecture, he developed controlled operator K-theory.
In the mathematical literature, several concepts are named after him, including Yu's property A and Yu's localization algebra.Yu has delivered invited addresses at the American Mathematical Society meeting in 1999, and at the International Congress of Mathematicians in Madrid in 2006.
He was a plenary speaker at the Topology Festival in 2002 and the Geometry Festival in 2007.
He is an editor of the Journal of Noncommutative Geometry, the Annals of K-Theory, the Journal of Topology and Analysis, and the Kyoto Journal of Mathematics.