David Mumford
Encyclopedia
David Bryant Mumford is an American mathematician
known for distinguished work in algebraic geometry
, and then for research into vision
and pattern theory
. He won the Fields Medal
and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science
. He is currently a University Professor in the Division of Applied Mathematics at Brown University
.
in England
, of an English father and American mother. His father William started an experimental school in Tanzania
and worked for the then newly created United Nations
.
In high school, he was a finalist in the prestigious Westinghouse Science Talent Search. After attending the Phillips Exeter Academy
, Mumford went to Harvard, where he became a student of Oscar Zariski
. At Harvard, he became a Putnam fellow in 1955 and 1956. He completed his Ph.D.
in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus.
He met his first wife, Erika Jentsch, at Radcliffe College
. After Erika died in 1988, he married his second wife, Jenifer Gordon.
He and Erika had four children. Steve
(born 1960) is a published artist residing in New York City
, Peter (born 1962) is a professional photographer and web developer living in Seattle, Jeremy (born 1969) is a historian, while Suchitra (born 1970, now Suchitra Baranoff) has worked for more than fifteen years in the field of international adoption.
s, with a theory summed up in his book Geometric Invariant Theory
, on the equations defining an abelian variety
, and on algebraic surface
s.
His books Abelian Varieties (with C. P. Ramanujam
) and Curves on an Algebraic Surface combined the old and new theories (to the disadvantage of the former, it has been claimed by Shreeram Abhyankar). His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique
, the only accessible introduction. They are now available as The Red Book of Varieties and Schemes (ISBN 3-540-63293-X).
Other work that was less thoroughly written up were lectures on varieties defined by quadric
s, and a study of Goro Shimura
's many papers from the 1960s.
Mumford’s research did much to revive the classical theory of theta functions, by showing that its algebraic content was large, and enough to support the main parts of the theory by reference to finite analogues of the Heisenberg group. This work on the equations defining abelian varieties
appeared in 1966–7. He published some further books of lectures on the theory.
He also was one of the founders of the toroidal embedding
theory; and sought to apply the theory to Gröbner basis
techniques, through students who worked in algebraic computation.
In the first Pathologies paper, Mumford finds an everywhere regular differential form on a smooth projective surface that is not closed, and shows that Hodge symmetry fails for classical Enriques surface
s in characteristic two. This second example is developed further in Mumford's third paper on classification of surfaces in characteristic p (written in collaboration with E. Bombieri). This pathology can now be explained in terms of the Picard scheme of the surface, and in particular, its failure to be a reduced scheme, which is a theme developed in Mumford's book "Lectures on Curves on an Algebraic Surface". Worse pathologies related to p-torsion in crystalline cohomology
were explored by Luc Illusie
(Ann. Sci. Ec. Norm. Sup. (4) 12 (1979), 501–661).
In the second Pathologies paper, Mumford gives a simple example of a surface in characteristic p where the geometric genus
is non-zero, but the second Betti number is equal to the rank of the Néron–Severi group
. He also conjectures that the Kodaira vanishing theorem is false for surfaces in characteristic p. In the third paper, he gives an example of a normal surface for which Kodaira vanishing fails. The first example of a smooth surface for which Kodaira vanishing fails was given by Michel Raynaud
in 1978.
parametrizing space curves of degree 14 and genus 24 has a multiple component. In the fourth Pathologies paper, he finds reduced and irreducible complete curves which are not specializations of non-singular curves.
These sorts of pathologies were considered to be fairly scarce when they first appeared. But recently, R. Vakil in a paper called "Murphy's law in algebraic geometry" has shown that Hilbert schemes of nice geometric objects can be arbitrarily "bad", with unlimited numbers of components and with arbitrarily large multiplicities (Invent. Math. 164 (2006), 569–590).
Once these adjustments are made, the surfaces are divided into four classes by their Kodaira dimension
, as in the complex case. The four classes are:
a) Kodaira dimension minus infinity. These are the ruled surface
s.
b) Kodaira dimension 0. These are the K3 surface
s, abelian surface
s, hyperelliptic and quasi-hyperelliptic surfaces, and Enriques surface
s. There are classical and non-classical examples in the last two Kodaira dimension zero cases.
c) Kodaira dimension 1. These are the elliptic and quasi-elliptic surfaces not contained in the last two groups.
d) Kodaira dimension 2. These are the surfaces of general type.
in 1974. He was a
MacArthur Fellow from 1987 to 1992. He won the Shaw Prize
in 2006. In 2007 he was awarded the Steele Prize for Mathematical Exposition by the American Mathematical Society
. In 2008 he was awarded the Wolf Prize; on receiving the prize in Jerusalem from Shimon Peres
, Mumford announced that he was donating half of the prize money to Birzeit University
in the Palestinian territories
and half to Gisha, an Israeli organization that advocates for the right to education and freedom of movement of Palestinians. In 2010 he was awarded the National Medal of Science
.
There is a long list of awards and honors besides the above, including
He was elected President of the International Mathematical Union
in 1995 and served from 1995 to 1999.
s: Indra's Pearls: The Vision of Felix Klein
(ISBN 0-521-35253-3).
His current area of work is pattern theory
.
He is color blind
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for distinguished work in algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and then for research into vision
Computer vision
Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...
and pattern theory
Pattern theory
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it...
. He won the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and...
. He is currently a University Professor in the Division of Applied Mathematics at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
.
Early life
Mumford was born in Worth, West SussexWorth, West Sussex
The civil parish of Worth, which includes the villages of Copthorne, West Sussex and Crawley Down, covers an area of and has a population of 9888 persons. The ecclesiastical parish was one of the larger West Sussex parishes, encompassing the entire area along the West Sussex/Surrey border between...
in England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
, of an English father and American mother. His father William started an experimental school in Tanzania
Tanzania
The United Republic of Tanzania is a country in East Africa bordered by Kenya and Uganda to the north, Rwanda, Burundi, and the Democratic Republic of the Congo to the west, and Zambia, Malawi, and Mozambique to the south. The country's eastern borders lie on the Indian Ocean.Tanzania is a state...
and worked for the then newly created United Nations
United Nations
The United Nations is an international organization whose stated aims are facilitating cooperation in international law, international security, economic development, social progress, human rights, and achievement of world peace...
.
In high school, he was a finalist in the prestigious Westinghouse Science Talent Search. After attending the Phillips Exeter Academy
Phillips Exeter Academy
Phillips Exeter Academy is a private secondary school located in Exeter, New Hampshire, in the United States.Exeter is noted for its application of Harkness education, a system based on a conference format of teacher and student interaction, similar to the Socratic method of learning through asking...
, Mumford went to Harvard, where he became a student of Oscar Zariski
Oscar Zariski
Oscar Zariski was a Russian mathematician and one of the most influential algebraic geometers of the 20th century.-Education:...
. At Harvard, he became a Putnam fellow in 1955 and 1956. He completed his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus.
He met his first wife, Erika Jentsch, at Radcliffe College
Radcliffe College
Radcliffe College was a women's liberal arts college in Cambridge, Massachusetts, and was the coordinate college for Harvard University. It was also one of the Seven Sisters colleges. Radcliffe College conferred joint Harvard-Radcliffe diplomas beginning in 1963 and a formal merger agreement with...
. After Erika died in 1988, he married his second wife, Jenifer Gordon.
He and Erika had four children. Steve
Steve Mumford
Steve Mumford is a contemporary American painter. His practice has lately included the depiction of scenes from the ongoing American wars in Iraq and Afghanistan...
(born 1960) is a published artist residing in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, Peter (born 1962) is a professional photographer and web developer living in Seattle, Jeremy (born 1969) is a historian, while Suchitra (born 1970, now Suchitra Baranoff) has worked for more than fifteen years in the field of international adoption.
Work in algebraic geometry
Mumford's work in geometry always combined the traditional geometric insights with the latest algebraic techniques. He published on moduli spaceModuli space
In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects...
s, with a theory summed up in his book Geometric Invariant Theory
Geometric invariant theory
In mathematics Geometric invariant theory is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces...
, on the equations defining an abelian variety
Abelian variety
In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions...
, and on algebraic surface
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two and so of dimension four as a smooth manifold.The theory of algebraic surfaces is much more complicated than that...
s.
His books Abelian Varieties (with C. P. Ramanujam
C. P. Ramanujam
Chakravarthi Padmanabhan Ramanujam was an Indian mathematician who worked in the fields of number theory and algebraic geometry. He got elected Fellow of the Indian Academy of Sciences in 1973...
) and Curves on an Algebraic Surface combined the old and new theories (to the disadvantage of the former, it has been claimed by Shreeram Abhyankar). His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique
Éléments de géométrie algébrique
The Éléments de géométrie algébrique by Alexander Grothendieck , or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published from 1960 through 1967 by the Institut des Hautes Études Scientifiques...
, the only accessible introduction. They are now available as The Red Book of Varieties and Schemes (ISBN 3-540-63293-X).
Other work that was less thoroughly written up were lectures on varieties defined by quadric
Quadric
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in -dimensional space defined as the locus of zeros of a quadratic polynomial...
s, and a study of Goro Shimura
Goro Shimura
is a Japanese mathematician, and currently a professor emeritus of mathematics at Princeton University.Shimura was a colleague and a friend of Yutaka Taniyama...
's many papers from the 1960s.
Mumford’s research did much to revive the classical theory of theta functions, by showing that its algebraic content was large, and enough to support the main parts of the theory by reference to finite analogues of the Heisenberg group. This work on the equations defining abelian varieties
Equations defining abelian varieties
In mathematics, the concept of abelian variety is the higher-dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study because every abelian variety is a projective variety...
appeared in 1966–7. He published some further books of lectures on the theory.
He also was one of the founders of the toroidal embedding
Toric geometry
In algebraic geometry, a toric variety or torus embedding is a normal variety containing an algebraic torus as a dense subset, such that the action of the torus on itself extends to the whole variety.-The toric variety of a fan:...
theory; and sought to apply the theory to Gröbner basis
Gröbner basis
In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating subset of an ideal I in a polynomial ring R...
techniques, through students who worked in algebraic computation.
Work on pathologies in algebraic geometry
In a sequence of four papers published in the American Journal of Mathematics between 1961 and 1975, Mumford explored pathological behavior in algebraic geometry, that is, phenomena that would not arise if the world of algebraic geometry were as well-behaved as one might expect from looking at the simplest examples. These pathologies fall into two types: (a) bad behavior in characteristic p and (b) bad behavior in moduli spaces.Characteristic-p pathologies
Mumford's philosophy in characteristic p was as follows:- "A nonsingular characteristic p variety is analogous to a general non-Kähler complex manifold; in particular, a projective embedding of such a variety is not as strong as a Kähler metric on a complex manifold, and the Hodge–Lefschetz–Dolbeault theorems on sheaf cohomologySheaf cohomologyIn mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F...
break down in every possible way."
In the first Pathologies paper, Mumford finds an everywhere regular differential form on a smooth projective surface that is not closed, and shows that Hodge symmetry fails for classical Enriques surface
Enriques surface
In mathematics, Enriques surfaces, discovered by , are complex algebraic surfacessuch that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square...
s in characteristic two. This second example is developed further in Mumford's third paper on classification of surfaces in characteristic p (written in collaboration with E. Bombieri). This pathology can now be explained in terms of the Picard scheme of the surface, and in particular, its failure to be a reduced scheme, which is a theme developed in Mumford's book "Lectures on Curves on an Algebraic Surface". Worse pathologies related to p-torsion in crystalline cohomology
Crystalline cohomology
In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by and developed by . Its values are modules over rings of Witt vectors over the base field....
were explored by Luc Illusie
Luc Illusie
Luc Illusie is a French mathematician. He is a former student of École Normale Supérieure, and got his PhD under the supervision of Alexander Grothendieck. He is professor emeritus at the Paris-Sud 11 University. Illusie made notable contributions to algebraic geometry.-External links:*...
(Ann. Sci. Ec. Norm. Sup. (4) 12 (1979), 501–661).
In the second Pathologies paper, Mumford gives a simple example of a surface in characteristic p where the geometric genus
Geometric genus
In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds.-Definition:...
is non-zero, but the second Betti number is equal to the rank of the Néron–Severi group
Néron–Severi group
In algebraic geometry, the Néron–Severi group of a variety isthe group of divisors modulo algebraic equivalence; in other words it is the group of components of the Picard scheme of a variety. Its rank is called the Picard number...
. He also conjectures that the Kodaira vanishing theorem is false for surfaces in characteristic p. In the third paper, he gives an example of a normal surface for which Kodaira vanishing fails. The first example of a smooth surface for which Kodaira vanishing fails was given by Michel Raynaud
Michel Raynaud
Michel Raynaud is a French mathematician working in algebraic geometry. Since 1967 he has been a professor at Paris-Sud 11 University.In 1983 he published a proof of the Manin-Mumford conjecture....
in 1978.
Pathologies of moduli spaces
In the second Pathologies paper, Mumford finds that the Hilbert schemeHilbert scheme
In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space , refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials...
parametrizing space curves of degree 14 and genus 24 has a multiple component. In the fourth Pathologies paper, he finds reduced and irreducible complete curves which are not specializations of non-singular curves.
These sorts of pathologies were considered to be fairly scarce when they first appeared. But recently, R. Vakil in a paper called "Murphy's law in algebraic geometry" has shown that Hilbert schemes of nice geometric objects can be arbitrarily "bad", with unlimited numbers of components and with arbitrarily large multiplicities (Invent. Math. 164 (2006), 569–590).
Classification of surfaces
In three papers written between 1969 and 1976 (the last two in collaboration with E. Bombieri), Mumford extended the Enriques–Kodaira classification of smooth projective surfaces from the case of the complex groundfield to the case of an algebraically closed groundfield of characteristic p. The final answer turns out to be essentially as the answer in the complex case (though the methods employed are sometimes quite different), once two important adjustments are made. The first is that one may get "non-classical" surfaces, which come about when p-torsion in the Picard scheme degenerates to a non-reduced group scheme. The second is the possibility of obtaining quasi-elliptic surfaces in characteristics two and three. These are surfaces fibred over a curve where the general fibre is a curve of arithmetic genus one with a cusp.Once these adjustments are made, the surfaces are divided into four classes by their Kodaira dimension
Kodaira dimension
In algebraic geometry, the Kodaira dimension κ measures the size of the canonical model of a projective variety V.The definition of Kodaira dimension, named for Kunihiko Kodaira, and the notation κ were introduced in the seminar.-The plurigenera:...
, as in the complex case. The four classes are:
a) Kodaira dimension minus infinity. These are the ruled surface
Ruled surface
In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone...
s.
b) Kodaira dimension 0. These are the K3 surface
K3 surface
In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.In the Enriques-Kodaira classification of surfaces they form one of the 5 classes of surfaces of Kodaira dimension 0....
s, abelian surface
Abelian surface
In mathematics, an abelian surface is 2-dimensional abelian variety.One dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic...
s, hyperelliptic and quasi-hyperelliptic surfaces, and Enriques surface
Enriques surface
In mathematics, Enriques surfaces, discovered by , are complex algebraic surfacessuch that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square...
s. There are classical and non-classical examples in the last two Kodaira dimension zero cases.
c) Kodaira dimension 1. These are the elliptic and quasi-elliptic surfaces not contained in the last two groups.
d) Kodaira dimension 2. These are the surfaces of general type.
Awards and honors
Mumford was awarded a Fields MedalFields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1974. He was a
MacArthur Fellow from 1987 to 1992. He won the Shaw Prize
Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
in 2006. In 2007 he was awarded the Steele Prize for Mathematical Exposition by the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
. In 2008 he was awarded the Wolf Prize; on receiving the prize in Jerusalem from Shimon Peres
Shimon Peres
GCMG is the ninth President of the State of Israel. Peres served twice as the eighth Prime Minister of Israel and once as Interim Prime Minister, and has been a member of 12 cabinets in a political career spanning over 66 years...
, Mumford announced that he was donating half of the prize money to Birzeit University
Birzeit University
Birzeit University is a university located in Birzeit near Ramallah, Palestinian territories. BZU is among the foremost tertiary educational institutes in the Palestinian territories and has played a significant role in the Palestinian political dialogue.- History :The institution was originally...
in the Palestinian territories
Palestinian territories
The Palestinian territories comprise the West Bank and the Gaza Strip. Since the Palestinian Declaration of Independence in 1988, the region is today recognized by three-quarters of the world's countries as the State of Palestine or simply Palestine, although this status is not recognized by the...
and half to Gisha, an Israeli organization that advocates for the right to education and freedom of movement of Palestinians. In 2010 he was awarded the National Medal of Science
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and...
.
There is a long list of awards and honors besides the above, including
- Westinghouse Science Talent SearchIntel Science Talent SearchThe Intel Science Talent Search , known for its first 57 years as the Westinghouse Science Talent Search is a research-based science competition in the United States for high school seniors. It has been referred to as "the nation's oldest and most prestigious" science competition. In his speech...
finalist, 1953. - Junior FellowHarvard Society of FellowsThe Harvard Society of Fellows is a group of scholars selected at the beginning of their careers by Harvard University for extraordinary scholarly potential, upon whom distinctive academic and intellectual opportunities are bestowed in order to foster their individual growth and intellectual...
at Harvard from 1958 to 1961. - Elected to the National Academy of SciencesUnited States National Academy of SciencesThe National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1975. - Honorary Fellow from Tata Institute of Fundamental ResearchTata Institute of Fundamental ResearchThe Tata Institute of Fundamental Research is a research institution in India dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the Department of Atomic Energy of the Government of India. It is located at Navy Nagar, Colaba, Mumbai...
in 1978. - Honorary D. Sc. from the University of WarwickUniversity of WarwickThe University of Warwick is a public research university located in Coventry, United Kingdom...
in 1983. - Foreign Member of Accademia Nazionale dei LinceiAccademia dei LinceiThe Accademia dei Lincei, , is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy....
, RomeRomeRome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
, in 1991. - Honorary Member of London Mathematical SocietyLondon 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 1995. - Elected to the American Philosophical SocietyAmerican Philosophical SocietyThe American Philosophical Society, founded in 1743, and located in Philadelphia, Pa., is an eminent scholarly organization of international reputation, that promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications,...
in 1997. - Honorary D. Sc. from Norwegian University of Science and TechnologyNorwegian University of Science and TechnologyThe Norwegian University of Science and Technology , commonly known as NTNU, is located in Trondheim. NTNU is the second largest of the eight universities in Norway, and, as its name suggests, has the main national responsibility for higher education in engineering and technology...
in 2000. - Honorary D. Sc. from Rockefeller UniversityRockefeller UniversityThe Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
in 2001. - Longuet-Higgins PrizeLonguet-Higgins PrizeLonguet-Higgins Prize is an award given annually by the IEEE Computer Society on the Conference on Computer Vision and Pattern Recognition , for 'fundamental contributions in Computer Vision'. The award recognizes CVPR papers from ten years ago with fundamental impact on computer vision research....
in 2005 and 2009. - Foreign Member of The Royal Society in 2008.
- Foreign Member of the Norwegian Academy of Science and LettersNorwegian Academy of Science and LettersThe Norwegian Academy of Science and Letters is a learned society based in Oslo, Norway.-History:The University of Oslo was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Throndhjem had no university, but had a learned...
. - Honorary Doctorate from Brown UniversityBrown UniversityBrown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
in 2011.
He was elected President of the International Mathematical Union
International Mathematical Union
The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...
in 1995 and served from 1995 to 1999.
Current activity
In 2002, Mumford wrote a book with Caroline Series and David Wright on the visual geometry of limit setLimit set
In mathematics, especially in the study of dynamical systems, a limit set is the state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time...
s: Indra's Pearls: The Vision of Felix Klein
Indra's Pearls (book)
Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002....
(ISBN 0-521-35253-3).
His current area of work is pattern theory
Pattern theory
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it...
.
He is color blind
Color blindness
Color blindness or color vision deficiency is the inability or decreased ability to see color, or perceive color differences, under lighting conditions when color vision is not normally impaired...
.
External links
- Mumford's page at Brown University
- Critical ReviewCritical Review (Brown)The Critical Review is a student publication that produces reviews of course offerings at Brown University. The student group that produces it is also called the Critical Review. The reviews are written by Brown students from course evaluation questionnaires distributed to class members in the...
evaluations of Professor Mumford