Daniel Wise

Who is Daniel Wise?

Daniel T. Wise is an American mathematician who specializes in geometric group theory and 3-manifolds. He obtained his PhD from Princeton University in 1996 on the topic of “Non-positively curved squared complexes, aperiodic tilings, and non-residually finite groups.” He is a professor of mathematics at McGill University.

Wise's research has focused on the role of non-positively curved cube complexes within geometric group theory and their interplay with residual finiteness. His early work was taken to higher dimensions when he introduced with Frédéric Haglund the theory of special cube complexes. In 2009 he announced a solution to the virtually fibered conjecture for cusped hyperbolic 3-manifolds. This was a consequence of his work on the structure of groups with a quasiconvex hierarchy which proved the virtual specialness of a broad class of hyperbolic groups, and established a program for using cube complexes to understand many infinite groups. This subsequently played a key role in the proof of the Virtually Haken conjecture.