Daniel Wise (mathematician)

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Daniel Wise

Daniel T. Wise.jpg
Daniel T. Wise
Daniel T. Wise
Alma materPrinceton University (PhD)
AwardsCRM-Fields-PIMS prize
Scientific career
ThesisNon-positively curved squared complexes, aperiodic tilings, and non-residually finite groups (1996)
Doctoral advisorMartin Bridson[1]

Daniel T. Wise FRS FRSC (born January 24, 1971) is an American mathematician who specializes in geometric group theory and 3-manifolds. He is a professor of mathematics at McGill University.[2]


Wise obtained his Ph.D. from Princeton University in 1996 supervised by Martin Bridson[1] His thesis was titled non-positively curved squared complexes, aperiodic tilings, and non-residually finite groups.[1]

Career and research[edit]

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.[3] In 2009 he announced a solution to the virtually fibered conjecture for cusped hyperbolic 3-manifolds.[4] This was a consequence of his work on the structure of groups with a quasiconvex hierarchy[5] 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.

Selected publications[edit]

  • Wise, Daniel T (2004). "Cubulating Small Cancellation Groups". Geom. Funct. 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. arXiv:0908.3609. doi:10.1353/ajm.2012.0020.

Awards and honors[edit]

In 2016 he was awarded the Jeffery–Williams Prize[6] and the CRM-Fields-PIMS Prize.[7] In 2016 Wise was awarded a Guggenheim Fellowship.[8] He was elected a Fellow of the Royal Society of Canada (FRSC) in 2014 and a Fellow of the Royal Society (FRS) in 2018.[9] 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.[10]


  1. ^ a b c Daniel Wise at the Mathematics Genealogy Project
  2. ^ Wise, Daniel. "Home Page". www.math.mcgill.ca.
  3. ^ "Special Cube Complexes". Geometric and Functional Analysis. 17: 1551–1620. doi:10.1007/s00039-007-0629-4.
  4. ^ "Archived copy". Archived from the original on 2014-04-15. Retrieved 2013-01-16.
  5. ^ "Hierarchy.pdf". Google Docs.
  6. ^ "Daniel Wise wins the 2016 Jeffery-Williams Prize for a profound impact in mathematical research". cms.math.ca.
  7. ^ "2016 CRM - Fields - PIMS Prize Winner: Daniel Wise - Pacific Institute for the Mathematical Sciences - PIMS". www.pims.math.ca.
  8. ^ "John Simon Guggenheim Foundation - Daniel T. Wise". www.gf.org.
  9. ^ "Daniel Wise". royalsociety.org.
  10. ^ "Awards and Prizes" (PDF). www.ams.org. January 10, 2013.

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