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Alan Reid's research primarily focusses on [[low-dimensional topology]], [[hyperbolic manifold]]s and [[profinite group]]s. He proved that the [[Figure-eight knot (mathematics)|figure-eight knot]] is the only knot whose complement is an [[arithmetic hyperbolic 3-manifold]].<ref>{{Cite journal|url=https://doi.org/10.1112/jlms/s2-43.1.171 |title=Arithmeticity of knot complements|year=1991 |doi=10.1112/jlms/s2-43.1.171 |last1=Reid |first1=Alan W. |journal=Journal of the London Mathematical Society |pages=171–184 |url-access=subscription }}</ref> With [[Martin Bridson]], Ben McReynolds and Ryan Spitler, he found the first examples of non-elementary [[Kleinian group]]s which are determined by their finite quotients among [[finitely generated group|finitely generated]] [[residually finite group]]s.<ref>{{Cite journal | url= https://doi.org/10.4007/annals.2020.192.3.1 | title = Absolute profinite rigidity and hyperbolic geometry | year = 2020 | doi = 10.4007/annals.2020.192.3.1 | last1 = Bridson | first1 = M. A. | last2 = McReynolds | first2 = D. B. | last3 = Reid | first3 = A. W. | last4 = Spitler | first4 = R. | journal = Annals of Mathematics | volume = 192 | issue = 3 | arxiv = 1811.04394 | s2cid = 119327769 }}</ref> |
Alan Reid's research primarily focusses on [[low-dimensional topology]], [[hyperbolic manifold]]s and [[profinite group]]s. He proved that the [[Figure-eight knot (mathematics)|figure-eight knot]] is the only knot whose complement is an [[arithmetic hyperbolic 3-manifold]].<ref>{{Cite journal|url=https://doi.org/10.1112/jlms/s2-43.1.171 |title=Arithmeticity of knot complements|year=1991 |doi=10.1112/jlms/s2-43.1.171 |last1=Reid |first1=Alan W. |journal=Journal of the London Mathematical Society |pages=171–184 |url-access=subscription }}</ref> With [[Martin Bridson]], Ben McReynolds and Ryan Spitler, he found the first examples of non-elementary [[Kleinian group]]s which are determined by their finite quotients among [[finitely generated group|finitely generated]] [[residually finite group]]s.<ref>{{Cite journal | url= https://doi.org/10.4007/annals.2020.192.3.1 | title = Absolute profinite rigidity and hyperbolic geometry | year = 2020 | doi = 10.4007/annals.2020.192.3.1 | last1 = Bridson | first1 = M. A. | last2 = McReynolds | first2 = D. B. | last3 = Reid | first3 = A. W. | last4 = Spitler | first4 = R. | journal = Annals of Mathematics | volume = 192 | issue = 3 | arxiv = 1811.04394 | s2cid = 119327769 }}</ref> |
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He has published more than 100 papers,<ref>{{cite web | url=https://mathscinet.ams.org/mathscinet/MRAuthorID/146355 | title=MathSciNet }}</ref> and supervised 21 PhD students to completion as of 2023. |
He has published more than 100 papers,<ref>{{cite web | url=https://mathscinet.ams.org/mathscinet/MRAuthorID/146355 | title=MathSciNet }}</ref> and supervised 21 PhD students to completion as of 2023.<ref>{{cite web | url=https://mathgenealogy.org/id.php?id=36986 | title=Alan Reid - the Mathematics Genealogy Project }}</ref><ref>{{cite web | url=https://math.rice.edu/~ar99/vitae.html | title=Alan Reid: Short Vitae }}</ref> |
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===Notable publications=== |
===Notable publications=== |
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[[Category:20th-century Scottish mathematicians]] |
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[[Category:American topologists]] |
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[[Category:Rice University faculty]] |
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[[Category:Alumni of the University of Aberdeen]] |
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Latest revision as of 14:33, 9 November 2024
Alan William Reid | |
|---|---|
 | |
| Born | June 14, 1962 (age 62) |
| Nationality | Scottish American |
| Alma mater | University of Aberdeen |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Rice University University of Texas, Austin |
| Thesis | Arithmetic Kleinian Groups and their Fuchsian Subgroups (1988) |
| Doctoral advisor | Colin Maclachlan |
Alan William Reid (born June 14, 1962) is a Scottish-American mathematician working primarily with arithmetic hyperbolic 3-manifolds. He is the Edgar Odell Lovett Chair of mathematics at Rice University, 2017—present.[1]
Biography
[edit]Reid grew up in Buckie, Scotland.[2] He obtained his doctorate from the University of Aberdeen,[3] supervised by Colin Maclachlan,[4] on the topic of Arithmetic Kleinian Groups and their Fuchsian Subgroups. He was a Royal Society University Research Fellow at Cambridge 1992-96. He was awarded the Sloan Research Fellowship in 1997,[5] and became one of the (inaugural) Fellows of the American Mathematical Society in 2013.[6]
Research
[edit]Alan Reid's research primarily focusses on low-dimensional topology, hyperbolic manifolds and profinite groups. He proved that the figure-eight knot is the only knot whose complement is an arithmetic hyperbolic 3-manifold.[7] With Martin Bridson, Ben McReynolds and Ryan Spitler, he found the first examples of non-elementary Kleinian groups which are determined by their finite quotients among finitely generated residually finite groups.[8]
He has published more than 100 papers,[9] and supervised 21 PhD students to completion as of 2023.[10][11]
Notable publications
[edit]- MacLachlan, Colin; Reid, Alan W. (2003). The Arithmetic of Hyperbolic 3-Manifolds. Graduate Texts in Mathematics. Vol. 219. doi:10.1007/978-1-4757-6720-9. ISBN 978-1-4419-3122-1. with Colin Maclachlan.
Awards and honours
[edit]- Speaker at the 2018 International Congress of Mathematicians, Rio de Janeiro.[12]
- Pennzoil Company Regents Professor of Mathematics, University of Texas, Austin, 2011–2016.[13]
- Sir Edmund Whittaker Prize in 1993.[14]
References
[edit]- ^ "Edgar Odell Lovett Chair of mathematics, Rice University, 2017--present".
- ^ "Alan Reid profile, AIMatters Autumn 2013 p. 15" (PDF).
- ^ "Alan Reid: Ph D thesis". discover.libraryhub.jisc.ac.uk.
- ^ "Alan Reid - The Mathematics Genealogy Project". www.mathgenealogy.org.
- ^ "Fellows Database".
- ^ List of 2013 Fellows of the American Mathematical Society, retrieved 2022-06-25.
- ^ Reid, Alan W. (1991). "Arithmeticity of knot complements". Journal of the London Mathematical Society: 171–184. doi:10.1112/jlms/s2-43.1.171.
- ^ Bridson, M. A.; McReynolds, D. B.; Reid, A. W.; Spitler, R. (2020). "Absolute profinite rigidity and hyperbolic geometry". Annals of Mathematics. 192 (3). arXiv:1811.04394. doi:10.4007/annals.2020.192.3.1. S2CID 119327769.
- ^ "MathSciNet".
- ^ "Alan Reid - the Mathematics Genealogy Project".
- ^ "Alan Reid: Short Vitae".
- ^ "List of 2018 ICM speakers".
- ^ "Ohio State Collloquium website".
- ^ "Sir Edmund Whittaker Memorial Prize". Proceedings of the Edinburgh Mathematical Society. 37 (2): 359–360. June 1994. doi:10.1017/S0013091500006131. ISSN 1464-3839.
External links
[edit]
Categories:
- 20th-century Scottish mathematicians
- 21st-century Scottish mathematicians
- American topologists
- Rice University faculty
- Alumni of the University of Aberdeen
- Living people
- University of Texas at Austin faculty
- Scottish expatriates in the United States
- Fellows of the American Mathematical Society
- People from Buckie
- 1962 births