Alan William Reid (born June 14, 1962) is a Scottish-American mathematician working primarily with

arithmetic hyperbolic 3-manifold In mathematics, more precisely in group theory and hyperbolic geometry, Arithmetic Kleinian groups are a special class of Kleinian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. An arith ...

s. 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 (Rice University) is a Private university, private research university in Houston, Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranke ...

, 2017—present.

Biography

Reid grew up in

Buckie Buckie ( gd, Bucaidh) is a burgh town (defined as such in 1888) on the Moray Firth coast of Scotland. Historically in Banffshire, Buckie was the largest town in the county until the administrative area was abolished in 1975. The town is the ...

Scotland Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...

. He obtained his doctorate from the

University of Aberdeen The University of Aberdeen ( sco, University o' 'Aiberdeen; abbreviated as ''Aberd.'' in List of post-nominal letters (United Kingdom), post-nominals; gd, Oilthigh Obar Dheathain) is a public university, public research university in Aberdeen, Sc ...

, supervised by Colin Maclachlan, on the topic of ''Arithmetic Kleinian Groups and their Fuchsian Subgroups''. He was a Royal Society University Research Fellow at Cambridge 1992-96.

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 structure theory of 3-manifolds and 4-manifolds, knot th ...

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 both sailing and rock climbing as a method of stopping ropes from running out of retaining devices. Like the overhand knot, which will jam under st ...

is the only knot whose complement is an

. With

Martin Bridson Martin Robert Bridson is a Manx mathematician. He is the Whitehead Professor of Pure Mathematics at the University of Oxford, and President of the Clay Mathematics Institute. He was previously Head of Oxford's Mathematical Institute. He is a ...

, 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 {{unsourced, date=September 2022 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 finit ...

Notable publications

* with Colin Maclachlan.

Awards and honours

* Speaker at the 2018 International Congress of Mathematicians, Rio de Janeiro. * In 2013 he 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 * Fellows Auctioneers, established in 1876. *Fellowes, Inc., manufacturer of wo ...

. * 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 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