Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory.
Lackenby studied mathematics at the University of Cambridge beginning in 1990, and earned his Ph.D. in 1997, with a dissertation on Dehn Surgery and Unknotting Operations supervised by W. B. R. Lickorish. [1] After positions as Miller Research Fellow at the University of California, Berkeley and as Research Fellow at Cambridge, he joined Oxford as a Lecturer and Fellow of St Catherine's in 1999. He was promoted to Professor at Oxford in 2006. [2]
Lackenby's research contributions include a proof of a strengthened version of the 2π theorem on sufficient conditions for Dehn surgery to produce a hyperbolic manifold, [L00] a bound on the hyperbolic volume of a knot complement of an alternating knot, [L04] and a proof that every diagram of the unknot can be transformed into a diagram without crossings by only a polynomial number of Reidemeister moves. [L15] In February 2021 he announced a new unknot recognition algorithm that runs in quasi-polynomial time. [3]
Lackenby won the Whitehead Prize of the London Mathematical Society in 2003. [4] In 2006, he won the Philip Leverhulme Prize in mathematics and statistics. [5] He was an invited speaker at the International Congress of Mathematicians in 2010. [6]
L00. | Lackenby, Marc (2000), "Word hyperbolic Dehn surgery",
Inventiones Mathematicae, 140 (2): 243–282,
arXiv:
math/9808120,
Bibcode:
2000InMat.140..243L,
doi:
10.1007/s002220000047,
MR
1756996.
|
L04. | Lackenby, Marc (2004), "The volume of hyperbolic alternating link complements",
Proceedings of the London Mathematical Society, Third Series, 88 (1): 204–224,
arXiv:
math/0012185,
doi:
10.1112/S0024611503014291,
MR
2018964.
|
L15. | Lackenby, Marc (2015), "A polynomial upper bound on Reidemeister moves",
Annals of Mathematics, Second Series, 182 (2): 491–564,
arXiv:
1302.0180,
doi:
10.4007/annals.2015.182.2.3,
MR
3418524.
|
Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory.
Lackenby studied mathematics at the University of Cambridge beginning in 1990, and earned his Ph.D. in 1997, with a dissertation on Dehn Surgery and Unknotting Operations supervised by W. B. R. Lickorish. [1] After positions as Miller Research Fellow at the University of California, Berkeley and as Research Fellow at Cambridge, he joined Oxford as a Lecturer and Fellow of St Catherine's in 1999. He was promoted to Professor at Oxford in 2006. [2]
Lackenby's research contributions include a proof of a strengthened version of the 2π theorem on sufficient conditions for Dehn surgery to produce a hyperbolic manifold, [L00] a bound on the hyperbolic volume of a knot complement of an alternating knot, [L04] and a proof that every diagram of the unknot can be transformed into a diagram without crossings by only a polynomial number of Reidemeister moves. [L15] In February 2021 he announced a new unknot recognition algorithm that runs in quasi-polynomial time. [3]
Lackenby won the Whitehead Prize of the London Mathematical Society in 2003. [4] In 2006, he won the Philip Leverhulme Prize in mathematics and statistics. [5] He was an invited speaker at the International Congress of Mathematicians in 2010. [6]
L00. | Lackenby, Marc (2000), "Word hyperbolic Dehn surgery",
Inventiones Mathematicae, 140 (2): 243–282,
arXiv:
math/9808120,
Bibcode:
2000InMat.140..243L,
doi:
10.1007/s002220000047,
MR
1756996.
|
L04. | Lackenby, Marc (2004), "The volume of hyperbolic alternating link complements",
Proceedings of the London Mathematical Society, Third Series, 88 (1): 204–224,
arXiv:
math/0012185,
doi:
10.1112/S0024611503014291,
MR
2018964.
|
L15. | Lackenby, Marc (2015), "A polynomial upper bound on Reidemeister moves",
Annals of Mathematics, Second Series, 182 (2): 491–564,
arXiv:
1302.0180,
doi:
10.4007/annals.2015.182.2.3,
MR
3418524.
|