Daniel Wise

Daniel Wise

Daniel T. "Dani" Wise (* 1971 ) is an American mathematician who studies geometry (3-manifolds) and group theory.

Wise grew up in New York City, studied mathematics from 1989 at Yeshiva University with a bachelor's degree in 1991 and received his doctorate from Princeton University with Martin Bridson in 1996 ( Non-Positively Curved Squared Complexes, Aperiodic Tilings and Non-Residually Finite Groups ) . He was a post-doctoral student at the University of California, Berkeley in 1996/97 . In 1997 he became an assistant professor at Cornell University , was 2000-01 Visiting Assistant Professor at Brandeis University and from 2001 assistant professor , in 2004 associate professor and in 2009 professor at McGill University . In 2008/09 he was visiting professor at the Hebrew University .

He researches infinite groups with applications in geometry and topology , especially geometric group theory, metric spaces with non-positive curvature , 3-dimensional manifolds, residual finite groups, subgroup separability and coherent groups.

His work on cubic complexes is an essential building block in the proofs of various conjectures from 3-dimensional topology, in particular the virtual hook conjecture ( Ian Agol 2012), but also one of the last open conjectures by William Thurston from 1982 that every hyperbolic 3-manifold is virtually fibrous .

In 2013, he and Ian Agol received the Oswald Veblen Prize . He received the Veblen Prize “for his deep-seated work demonstrating subgroup separability for a large class of groups and for introducing and developing the theory of special cube complexes with Frédéric Haglund , which is of fundamental importance for the topology of 3-manifolds are". In 2014 he was elected a member of the Royal Society of Canada . For 2016 he was awarded the Jeffery Williams Prize and the CRM Fields PIMS Prize .

In 2014 he was an invited speaker at the ICM in Seoul (The cubical route to understanding groups). In 2018 Wise was elected to the Royal Society .

Works

• with F. Haglund: A combination theorem for special cube complexes , Annals of Mathematics 176-3, 1427-1482 (2012), pdf
• with F. Haglund: Special Cube Complexes , Geom. Funct. Analysis, Volume 17, 2008, pp. 1551-1620
• From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry , CBMS Regional Conference Series in Mathematics 2012; 141 pp; softcover, ISBN 0-8218-8800-5
• Subgroup separability of graphs of free groups with cyclic edge groups , Quarterly Journal of Mathematics, Volume 51, 2000, pp. 107-129
• Residual finiteness of negatively curved polygons of finite groups , Inventiones Mathematicae, Volume 149, 2002, pp. 579-617

Web links

• Homepage
• RAAGs over Riches , understandable presentation of Wise's work on special cubic complexes (Daniel Moskovich)
• Award ceremony at the AMS 2013, pdf

Individual evidence

1. ^ Mathematics Genealogy Project
2. ↑ The intersection of the subgroups of finite index is the trivial subgroup
3. ↑ Every finitely generated subgroup is the intersection of the subgroups of finite index
4. ↑ Every finitely generated subgroup is finitely presentable
5. ↑ From the abstract on Agol's proof of the virtual hook conjecture (PDF file; 814 kB): “ We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are separable. A consequence is that closed hyperbolic 3-manifolds have finite-sheeted hook covers, which resolves the virtual hook question of Waldhausen and Thurston's virtual fibering question. ”
6. ↑ Stefan Friedl, Thurston's Vision and the Virtual Fibering Theorem for 3-Manifolds, Annual Report DMV, 2014, Issue 4, pdf
7. ↑ “ for his deep work establishing subgroup separability (LERF) for a wide class of groups and for introducing and developing with Frédéric Haglund the theory of special cube complexes which are of fundamental importance for the topology of three-dimensional manifolds. ” Laudation Veblen Prize
8. ↑ RSC Class of 2014. (PDF) (No longer available online.) Archived from the original on July 7, 2015 ; accessed on September 13, 2016 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.