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 Edgar Odell Lovett (April 14, 1871 – August 13, 1957) was an American educator and education administrator. He was the first president of Rice Institute (now Rice University) in Houston, Texas. Lovett was recommended to the post by Woodr ...

Chair of mathematics at

Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...

, 2017—present.

Biography

Reid grew up in

Buckie Buckie () is a burgh town (defined as such in List of burghs in Scotland, 1888) on the Moray Firth coast of Scotland. Counties of Scotland, Historically in Banffshire, Buckie was the largest town in the county until the administrative area was ...

Scotland Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...

. He obtained his doctorate from the

University of Aberdeen The University of Aberdeen (abbreviated ''Aberd.'' in List of post-nominal letters (United Kingdom), post-nominals; ) is a public university, public research university in Aberdeen, Scotland. It was founded in 1495 when William Elphinstone, Bis ...

, supervised by Colin Maclachlan, on the topic of ''Arithmetic Kleinian Groups and their Fuchsian Subgroups''. He was a

Royal Society University Research Fellow __NOTOC__ The Royal Society University Research Fellowship (URF) is a research fellowship awarded to outstanding early career scientists in the United Kingdom who are judged by the Royal Society The Royal Society, formally The Royal Society ...

at Cambridge 1992-96. He was awarded the

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in 1997, and became one of the (inaugural)

Fellows of the American Mathematical Society Fellows may refer to Fellow, in plural form. Fellows or Fellowes may also refer to: Places *Fellows, California, USA *Fellows, Wisconsin, ghost town, USA Other uses * Fellowes, Inc., manufacturer of workspace products *Fellows, a partner in the f ...

in 2013.

Research

Alan Reid's research primarily focusses on

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, ...

hyperbolic manifold In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in dimensions 2 and 3, where they are called hyperbolic surfaces and hyperbolic 3-manifolds, res ...

s and

profinite group In mathematics, a profinite group is a topological group that is in a certain sense assembled from a system of finite groups. The idea of using a profinite group is to provide a "uniform", or "synoptic", view of an entire system of finite groups. ...

s. He proved that the

figure-eight knot The figure-eight knot or figure-of-eight knot is a type of stopper knot. It is very important in sailing, rock climbing and caving as a method of stopping ropes from running out of retaining devices. Like the overhand knot, which will jam under ...

is the only knot whose complement is an arithmetic hyperbolic 3-manifold. With Martin Bridson, Ben McReynolds and Ryan Spitler, he found the first examples of non-elementary

Kleinian group In mathematics, a Kleinian group is a discrete subgroup of the group (mathematics), group of orientation-preserving Isometry, isometries of hyperbolic 3-space . The latter, identifiable with PSL(2,C), , is the quotient group of the 2 by 2 complex ...

s which are determined by their finite quotients among finitely generated

residually finite group In the mathematical field of group theory, a group ''G'' is residually finite or finitely approximable if for every element ''g'' that is not the identity in ''G'' there is a homomorphism ''h'' from ''G'' to a finite group, such that :h(g) \neq 1 ...

s. He has published more than 100 papers, and supervised 21 PhD students to completion as of 2023.

Notable publications

* with Colin Maclachlan.

Awards and honours

* Speaker at the 2018 International Congress of Mathematicians, Rio de Janeiro. * Pennzoil Company Regents Professor of Mathematics, University of Texas, Austin, 2011–2016. * Sir Edmund Whittaker Prize in 1993.

References

External links

* {{DEFAULTSORT:Reid, Alan William 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