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Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory
Marc_Lackenby
Unique knot with a crossing number of four
451–478. MR 1869847 Marc Lackenby, Word hyperbolic Dehn surgery, Inventiones Mathematicae 140 (2000), no. 2, 243–282. MR 1756996 Marc Lackenby and Robert Meyerhoff
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Study of mathematical knots
unknotting problem, is of particular interest (Hoste 2005). In February 2021 Marc Lackenby announced a new unknot recognition algorithm that runs in quasi-polynomial
Knot_theory
Computational complexity class
recognizing whether a knot diagram describes the unknot, announced by Marc Lackenby in 2021. Quasi-polynomial time has also been used to study approximation
Quasi-polynomial_time
Generalization of Dehn's lemma in the topology of 3-manifolds
Haken hierarchy. Proofs were later written up, by Klaus Johannson, Marc Lackenby, and Iain Aitchison with Hyam Rubinstein. One easy corollary of the
Loop_theorem
exceptional surgeries of any hyperbolic knot complement. This was proved by Marc Lackenby and Rob Meyerhoff, who show that the number of exceptional slopes is
Hyperbolic_Dehn_surgery
Integer-valued knot invariant; least number of crossings in a knot diagram
more generally, adequate knot), or if the summands are torus knots. Marc Lackenby has also given a proof that there is a constant N > 1 such that 1/N(cr(K1)
Crossing_number_(knot_theory)
Gives sufficient condition for Dehn filling to result in a negatively curved 3-manifold
This result was later improved independently by Ian Agol (2000) and Marc Lackenby (2000) with the 6 theorem. The "6 theorem" states that Dehn filling
2π_theorem
Determining whether a knot is the unknot
problem is in co-NP, and in 2016, Marc Lackenby provided an unconditional proof of co-NP membership. In 2021, Lackenby announced an unknot recognition algorithm
Unknotting_problem
London Mathematical Society prize
Alessio Corti, Marianna Csörnyei, C. Teleman [de] 2003 N. Dorey, T. Hall, Marc Lackenby, M. Nazarov 2004 Mark Ainsworth, Vladimir Markovic, Richard Thomas,
Whitehead_Prize
Kuijlaars Shrawan Kumar Karl Kunisch Antti Kupiainen Wolfgang Lück Marc Lackenby Sergey Lando [ru] Erez Lapid Yoram Last Bernard Leclerc Chiu-Chu Melissa
List of International Congresses of Mathematicians Plenary and Invited Speakers
List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
Thus hyperbolic volume is an invariant of many alternating links. Marc Lackenby has shown that the volume has upper and lower linear bounds as functions
Alternating_knot
British mathematician (born 1938)
(1991) Carl B. Allendoerfer Award (1989) Scientific career Fields Mathematician Doctoral advisor Erik Christopher Zeeman Doctoral students Marc Lackenby
W._B._R._Lickorish
Academic journal
Copenhagen) Misha Kapovich (UC Davis) Frances Kirwan (University of Oxford) Marc Lackenby (University of Oxford) Oscar Randal-Williams (University of Cambridge)
Journal_of_Topology
One of three types of isotopy-preserving local changes to a knot diagram
doi:10.2307/1968399, JSTOR 1968399, MR 1502807 Coward, Alexander; Lackenby, Marc (2014), "An upper bound on Reidemeister moves", American Journal of
Reidemeister_move
American mathematician
Differential Geometry. 34 (2): 539–560. doi:10.4310/jdg/1214447220. Lackenby, Marc (1997-08-01). "Surfaces, surgery and unknotting operations". Mathematische
Martin_Scharlemann
Measure of whether or not a graph has a "bottleneck"
doi:10.1088/1742-5468/2006/08/P08007. ISSN 1742-5468. S2CID 16192273. Lackenby, Marc (2006). "Heegaard splittings, the virtually Haken conjecture and Property
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Complexity class of problems
Research. 36 (4): 743–753. doi:10.1287/moor.1110.0515. MR 2855867. Lackenby, Marc (2021). "The efficient certification of knottedness and Thurston norm"
NP-intermediate
Integral polynomial
Tanburn, Richard; Battaglia, Peter; Blundell, Charles; Juhász, András; Lackenby, Marc; Williamson, Geordie; Hassabis, Demis; Kohli, Pushmeet (Dec 5, 2021)
Kazhdan–Lusztig_polynomial
German mathematician (1928–2022)
AMS, p. xv, ISBN 0-8218-5103-9 Callahan, Patrick; Kapovich, Ilya; Lackenby, Marc; Shalen, Peter; Wilson, Robin (October 2023). "Wolfgang Haken, 1928–2022"
Wolfgang_Haken
Loop seen as a trivial knot
Taylor; Blackwell, Sam; Davies, Alex; Edlich, Thomas; Juhász, András; Lackenby, Marc; Tomašev, Nenad; Zheng, Daniel (2025). "The unknotting number, hard
Unknot
Ian Agol, Daniel Groves, and Jason Manning: 1045–1087. MR 3104553. Lackenby, Marc; Long, Darren D.; Reid, Alan W. (2008). "Covering spaces of arithmetic
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
Subfield of mathematical topology
185–211, arXiv:math/9807016, doi:10.1145/301970.301971, S2CID 125854 Lackenby, Marc (2021), "The efficient certification of Knottedness and Thurston norm"
Computational_topology
Klainerman, Sergiu 1978–1980 New York University, 1978 Princeton University Lackenby, Marc 1997–1998 University of Cambridge, 1997 University of Oxford Langlands
List of Miller Research Fellows
List_of_Miller_Research_Fellows
Trondheim, Norway Sam Rankin Eric Cox Ryan Hazlitt-Black Tim Weeks Jacob Lackenby Australia Thomas Reed Neil Imada Preston Ballard Miles Reed Maple Ridge
List of teams in the 2022–23 curling season
List_of_teams_in_the_2022–23_curling_season
Multinational steelmaking company
1967 until its closure in 1992. Teesside Cast Products, blast furnaces at Lackenby, Redcar, North Yorkshire, UK – mothballed 2010, sold 2011 to SSI, closed
Tata_Steel_Europe
Kraus, MA, Fellow of Corpus Christi College: Professor of Physics M. Lackenby, MA, DPhil, Fellow of St Catherine's College: Professor of Mathematics
Titles of distinction awarded by the University of Oxford
Titles_of_distinction_awarded_by_the_University_of_Oxford
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MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
MARC LACKENBY
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