Professor of Mathematics
Personal Website:
+44 1865 273561
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
A polynomial upper bound on Reidemeister moves
Annals of Mathematics
issue 2
volume 182
page 491-564
(September 2015)
Full text available
The maximal number of exceptional Dehn surgeries
Inventiones Mathematicae
issue 2
volume 191
page 341-382
(1 January 2013)
The volume of hyperbolic alternating link complements
Proceedings of the London Mathematical Society
issue 1
volume 88
page 204-224
(13 January 2004)
Word hyperbolic Dehn surgery
INVENTIONES MATHEMATICAE
issue 2
volume 140
page 243-282
(May 2000)
Full text available
The crossing number of composite knots
JOURNAL OF TOPOLOGY
issue 4
volume 2
page 747-768
(2009)
Full text available
Recent Publications:
ALTERNATING LINKS AND DEFINITE SURFACES
DUKE MATHEMATICAL JOURNAL
issue 11
volume 166
page 2133-2151
(15 August 2017)
Full text available
Cusp volumes of alternating knots
Geometry and Topology
(23 October 2014)
Full text available
Finding disjoint surfaces in 3-manifolds
Geometriae Dedicata
issue 1
volume 170
page 385-401
(1 January 2014)
The maximal number of exceptional Dehn surgeries
Inventiones Mathematicae
(5 April 2012)
Full text available
An upper bound on Reidemeister moves
American Journal of Mathematics
(11 April 2011)
Full text available
Research Interests:
Topology, geometry and group theory
Further Details:
Editor of "Journal of Topology"
Editor of "Groups, Geometry and Dynamics"
Editor of "Journal of the LMS" (2008-2013)
Prizes, Awards, and Scholarships:
LMS Whitehead Prize 2003
EPSRC Advanced Research Fellowship 2004-09
Philip Leverhulme Prize 2006
Invited speaker, ICM 2010