Daniel Wise (mathematician)
Daniel T. Wise (born January 24, 1971) is an American mathematician who specializes in geometric group theory and 3-manifolds. He obtained his Ph.D. 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.
For the theory of special cube complexes and his establishment of subgroup separability for a wide class of groups, Daniel Wise together with Ian Agol was awarded in 2013 the Oswald Veblen Prize in Geometry.
- Wise, Daniel T (2004). "Cubulating Small Cancellation Groups". Geom. Func. Anal. 14: 150–214. doi:10.1007/s00039-004-0454-y.
- Wise, Daniel T (2002). "The residual finiteness of negatively curved polygons of finite groups". Invent. Math. 149 (3): 579–617. doi:10.1007/s002220200224.
- Haglund, Frédéric; Wise, Daniel T. (2012). "A combination theorem for special cube complexes". Annals of Mathematics. 176 (3): 1427–1482. doi:10.4007/annals.2012.176.3.2.
- Wise, Daniel T. From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups and Cubical Geometry (AMS Lecture Notes, 2012).
- Bergeron, Nicolas; Wise, Daniel T. (2012). "A Boundary Criterion for Cubulation" (PDF). AJM. 134 (3): 843–859. doi:10.1353/ajm.2012.0020.
- "Special Cube Complexes". Geometric and Functional Analysis. 17: 1551–1620. doi:10.1007/s00039-007-0629-4.
- The Structure of Groups with a Quasiconvex Hierarchy
- Daniel Wise's webpage
- 2011 NSF-CBMS conference
- Klarreich, Erica (2 October 2012), "Getting Into Shapes: From Hyperbolic Geometry to Cube Complexes and Back", Quanta Magazine (An expository account of the resolution of the Virtual Haken conjecture)