Shahn Majid
Encyclopedia
Born in 1960 in Patna
, Bihar, India Shahn Majid is an English
pure mathematician and theoretical physicist, trained at Cambridge University and Harvard and since 2001 a Professor of Mathematics at the School of Mathematical Sciences, Queen Mary, University of London
.
Majid is best known for his pioneering work on quantum group
s where he introduced one of the two main known classes of these objects and worked on all aspects of their theory. His 1995 text book Foundations of Quantum Group Theory is a standard text still used by researchers today. He also pioneered a quantum groups approach to noncommutative geometry
and the use of such methods as a route to quantum gravity
, leading in 1994 to the first model with testable predictions of quantum spacetime
. He is also known for a range of results in algebra and category theory, notably for his theory of braided Hopf algebra
s and for a new view of the octonions. Although many regard Majid as a pure mathematician, his motivation and early training was in theoretical physics and pure mathematics merely represents a path in his lifelong search for the `true nature of physical reality'.
In 2008 he edited and co-authored an ambitious book of essays On Space and Time along with Alain Connes
, Roger Penrose
, John Polkinghorne
, Michal Heller and Andrew Taylor in which the authors aim to expose the frontier of scientific research on the small and large scale structure of the Universe to a general but scientifically interested audience.
and MIT trained pure mathematician based at King's College London
, and has two children.
following the Mathematics Tripos and based at Emmanuel College, Cambridge
. In 1983 a Herschel Smith Scholarship took him to Harvard where he was a tutor at Eliot House
while engaged in his PhD jointly between the physics and pure mathematics departments, under Arthur Jaffe
and Clifford Taubes
respectively. Armed with his PhD in 1988, his first job was as a 1-year postdoc at the University of Swansea before moving on a Drapers Fellowship to Pembroke College, Cambridge
, where he remained a Fellow until his move to Queen Mary in 1999. The 10 years of research based in Cambridge University, DAMTP included two years as a visiting scholar back at Harvard and a variety of research fellowships including a Royal Society
University Research Fellowship. In 1993 he was awarded a one-time Konrad Bleuler Medal by an international conference. He has been visiting professor at the Perimeter Institute, Oxford University and Cambridge University as well as principal organiser along with Alain Connes and Albert Schwarz of a 6-month programme on noncommutative geometry at the Isaac Newton Institute
in 2006. In 2009 he was a Leverhulme Trust
Senior Research Fellow.
on the space of loops on a manifold and their quantisation as noncommutative geometry, a novel `infinite spin' limit for handling infinities in quantum field theory and an infinitesimal explanation of quark confinement.
His 1988 PhD thesis introduced a `bicrossproduct' type of quantum group
at a time when few such objects were known. Half way through his PhD research Vladimir Drinfeld and Michio Jimbo
found another and more popular class of these objects, but the bicrossproduct ones have had a resurgence of interest in recent years. Majid rapidly established himself as a leading authority on all types of quantum groups and developed a distinctive Hopf algebra
ic approach to them, including well-known results on the quantum double and a duality construction for a monoidal category
. His 1998 lectures on the topic in the Mathematical Tripos of the University of Cambridge were published by the London Mathematical Society
.
In the 1990s Majid introduced the theory of braided groups or braided Hopf algebra
s as the true objects underlying
-deformations. He proved the main theorems in the field of `transmutation' and `bosonisation' and constructed the first and still main examples of the theory, including quantum planes as an additive braided groups. Other well-known work includes a picture of the octonions as associative in a certain symmetric monoidal monoidal category.
Also in the 1990s he pioneered the theory and first models of noncommutative or quantum spacetime
s. The 1994 Majid-Ruegg model in particular turned out to be testable by data now being collected by the GLAST-Fermi gamma ray space telescope. Whether his model is confirmed or not, the most important thing, according to Majid, is that unlike much of modern theoretical physics, it is testable. Recent works include theorems pointing to a new field of nonassociative geometry, noncommutative gravity and (2+1)-dimensional quantum gravity.
This revealing quote from page 112 of On Space and Time was presented as reply to physicists who attack mathematicians while turning to maths books for structures to use in their theories, as if mathematics is a resource rather than part of the creative process. The subtle interplay between the creativity of pure mathematics and the fact-driven agenda of physics form the basis of a general philosophy of Relative Realism in which Majid argues that the nature of Physical Reality is not fundamentally different from the way that topics in Pure Mathematics are on the one hand created by definitions and on the other hand `out there' waiting to be invented. Majid gives the more everyday example of the way that the reality experienced in a game of chess is created by the rules of chess and the choice to abide by them while at the same time, on another level, the rules of chess were themselves a reality waiting to be discovered by those seeking to invent board games. The general picture leads to a dualism between experiment and theory or `principle of representation-theoretic self-duality' in which Majid argues that `the search for the ultimate theory of physics is
the search for self-dual structures in a self-dual category'. Although not accepted by professional philosophers of science, the philosophy has provided a point of view behind most of his research work.
Patna
Paṭnā , is the capital of the Indian state of Bihar and the second largest city in Eastern India . Patna is one of the oldest continuously inhabited places in the world...
, Bihar, India Shahn Majid is an English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
pure mathematician and theoretical physicist, trained at Cambridge University and Harvard and since 2001 a Professor of Mathematics at the School of Mathematical Sciences, Queen Mary, University of London
Queen Mary, University of London
Queen Mary, University of London is a public research university located in London, United Kingdom and a constituent college of the federal University of London...
.
Majid is best known for his pioneering work on quantum group
Quantum group
In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra...
s where he introduced one of the two main known classes of these objects and worked on all aspects of their theory. His 1995 text book Foundations of Quantum Group Theory is a standard text still used by researchers today. He also pioneered a quantum groups approach to noncommutative geometry
Noncommutative geometry
Noncommutative geometry is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative algebras of functions...
and the use of such methods as a route to quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
, leading in 1994 to the first model with testable predictions of quantum spacetime
Quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra...
. He is also known for a range of results in algebra and category theory, notably for his theory of braided Hopf algebra
Braided Hopf algebra
In mathematics a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfel'd category of a Hopf algebra H, particurlarly the Nichols algebra of a braided vectorspace in that category.The notion should not be confused...
s and for a new view of the octonions. Although many regard Majid as a pure mathematician, his motivation and early training was in theoretical physics and pure mathematics merely represents a path in his lifelong search for the `true nature of physical reality'.
In 2008 he edited and co-authored an ambitious book of essays On Space and Time along with Alain Connes
Alain Connes
Alain Connes is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.-Work:...
, Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
, John Polkinghorne
John Polkinghorne
John Charlton Polkinghorne KBE FRS is an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest...
, Michal Heller and Andrew Taylor in which the authors aim to expose the frontier of scientific research on the small and large scale structure of the Universe to a general but scientifically interested audience.
Personal life
At age five he moved with his family from India to the UK, where his father went on to become a noted orthopaedic surgeon and his mother a primary school teacher and a published poet. He grew up in Hampstead, London, where he now lives, is married to Konstanze Rietsch, a University of ViennaUniversity of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
and MIT trained pure mathematician based at King's College London
King's College London
King's College London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. King's has a claim to being the third oldest university in England, having been founded by King George IV and the Duke of Wellington in 1829, and...
, and has two children.
Education and career
He did his B.A. and Part III diploma at the University of CambridgeUniversity of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
following the Mathematics Tripos and based at Emmanuel College, Cambridge
Emmanuel College, Cambridge
Emmanuel College is a constituent college of the University of Cambridge.The college was founded in 1584 by Sir Walter Mildmay on the site of a Dominican friary...
. In 1983 a Herschel Smith Scholarship took him to Harvard where he was a tutor at Eliot House
Eliot House
Eliot House is one of twelve residential houses for upperclassmen at Harvard University and one of the seven original houses at the College. Opened in 1931, the house was named after Charles William Eliot, who served as president of the university for forty years .-Traditions:Before Harvard opted...
while engaged in his PhD jointly between the physics and pure mathematics departments, under Arthur Jaffe
Arthur Jaffe
Arthur Jaffe is an American mathematical physicist and a professor at Harvard University. Born on December 22, 1937 he attended Princeton University as an undergraduate obtaining a degree in chemistry, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics...
and Clifford Taubes
Clifford Taubes
Clifford Henry Taubes is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology.-Early career:Taubes received his Ph.D...
respectively. Armed with his PhD in 1988, his first job was as a 1-year postdoc at the University of Swansea before moving on a Drapers Fellowship to Pembroke College, Cambridge
Pembroke College, Cambridge
Pembroke College is a constituent college of the University of Cambridge, England.The college has over seven hundred students and fellows, and is the third oldest college of the university. Physically, it is one of the university's larger colleges, with buildings from almost every century since its...
, where he remained a Fellow until his move to Queen Mary in 1999. The 10 years of research based in Cambridge University, DAMTP included two years as a visiting scholar back at Harvard and a variety of research fellowships including a Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
University Research Fellowship. In 1993 he was awarded a one-time Konrad Bleuler Medal by an international conference. He has been visiting professor at the Perimeter Institute, Oxford University and Cambridge University as well as principal organiser along with Alain Connes and Albert Schwarz of a 6-month programme on noncommutative geometry at the Isaac Newton Institute
Isaac Newton Institute
The Isaac Newton Institute for Mathematical Sciences is an international research institute for mathematics and theoretical physics. Part of the University of Cambridge, it is named after one of the university's most illustrious figures, the mathematician and natural philosopher Sir Isaac Newton....
in 2006. In 2009 he was a Leverhulme Trust
Leverhulme Trust
The Leverhulme Trust was established in 1925 under the will of the First Viscount Leverhulme, William Hesketh Lever, with the instruction that its resources should be used to support "scholarships for the purposes of research and education."...
Senior Research Fellow.
Scientific Works
Majid wrote several early papers before his more established PhD work. These included work on gauge fields as Fourier TransformFourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
on the space of loops on a manifold and their quantisation as noncommutative geometry, a novel `infinite spin' limit for handling infinities in quantum field theory and an infinitesimal explanation of quark confinement.
His 1988 PhD thesis introduced a `bicrossproduct' type of quantum group
Quantum group
In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra...
at a time when few such objects were known. Half way through his PhD research Vladimir Drinfeld and Michio Jimbo
Michio Jimbo
is a Japanese mathematician, currently a professor at the University of Tokyo. He is a grandson of the linguist Kaku Jimbo.After graduating from the University of Tokyo in 1974, he studied under Mikio Sato at the Research Institute for Mathematical Sciences in Kyoto University...
found another and more popular class of these objects, but the bicrossproduct ones have had a resurgence of interest in recent years. Majid rapidly established himself as a leading authority on all types of quantum groups and developed a distinctive Hopf algebra
Hopf algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an algebra and a coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.Hopf algebras occur naturally...
ic approach to them, including well-known results on the quantum double and a duality construction for a monoidal category
Monoidal category
In mathematics, a monoidal category is a category C equipped with a bifunctorwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism...
. His 1998 lectures on the topic in the Mathematical Tripos of the University of Cambridge were published by the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
.
In the 1990s Majid introduced the theory of braided groups or braided Hopf algebra
Braided Hopf algebra
In mathematics a braided Hopf algebra is a Hopf algebra in a braided monoidal category. The most common braided Hopf algebras are objects in a Yetter–Drinfel'd category of a Hopf algebra H, particurlarly the Nichols algebra of a braided vectorspace in that category.The notion should not be confused...
s as the true objects underlying
-deformations. He proved the main theorems in the field of `transmutation' and `bosonisation' and constructed the first and still main examples of the theory, including quantum planes as an additive braided groups. Other well-known work includes a picture of the octonions as associative in a certain symmetric monoidal monoidal category.Also in the 1990s he pioneered the theory and first models of noncommutative or quantum spacetime
Quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra...
s. The 1994 Majid-Ruegg model in particular turned out to be testable by data now being collected by the GLAST-Fermi gamma ray space telescope. Whether his model is confirmed or not, the most important thing, according to Majid, is that unlike much of modern theoretical physics, it is testable. Recent works include theorems pointing to a new field of nonassociative geometry, noncommutative gravity and (2+1)-dimensional quantum gravity.
A philosophy of Relative Realism
"Nature does not necessarily use the maths already in maths books, hence theoretical physicists should be prepared to explore ... all of pure mathematics"
This revealing quote from page 112 of On Space and Time was presented as reply to physicists who attack mathematicians while turning to maths books for structures to use in their theories, as if mathematics is a resource rather than part of the creative process. The subtle interplay between the creativity of pure mathematics and the fact-driven agenda of physics form the basis of a general philosophy of Relative Realism in which Majid argues that the nature of Physical Reality is not fundamentally different from the way that topics in Pure Mathematics are on the one hand created by definitions and on the other hand `out there' waiting to be invented. Majid gives the more everyday example of the way that the reality experienced in a game of chess is created by the rules of chess and the choice to abide by them while at the same time, on another level, the rules of chess were themselves a reality waiting to be discovered by those seeking to invent board games. The general picture leads to a dualism between experiment and theory or `principle of representation-theoretic self-duality' in which Majid argues that `the search for the ultimate theory of physics is
the search for self-dual structures in a self-dual category'. Although not accepted by professional philosophers of science, the philosophy has provided a point of view behind most of his research work.
Publications
Numerous research publications and review articles, and the following three books:External links
- Shahn Majid's Academic Home Page
- Partial list of downloadable research articles
- Talk at the 2009 Cambridge Science Festival about the origin of time
- Read the Preface of On Space and Time
- Amapaedia entry for On Space and Time
- 12 weekly blog posts by Shahn Majid at Cambridge University Press in 2008
- 2007 Podcast by Plus Magazine featuring Shahn Majid
- 2007 Article based on an interview with Shahn Majid by Plus Magazine
- 1998 feature in a photographic exhibition Faces of Mathematics
- Read Shahn Majid's philosophy essay on Physics v Maths circa 1997
- German article about Konrad Bleuler