Augustin Banyaga
Encyclopedia
Augustin Banyaga is a Rwandan-born America
n mathematician
whose research fields include symplectic topology
and contact geometry
. He is currently a Professor of Mathematics at Pennsylvania State University
.
degree in 1976 at the University of Geneva
under the supervision of André Haefliger
. He was a member of the Institute for Advanced Study
in Princeton, New Jersey
(1977–1978), Benjamin Peirce
Assistant Professor at Harvard University
(1978–1982), and Assistant Professor at Boston University
(1982–1984), before joining the faculty at Pennsylvania State University in 1984 as Associate Professor. He was promoted to Full Professor in 1992.
He has made significant contributions in symplectic topology, especially on the structure of groups
of diffeomorphism
s preserving a symplectic form (symplectomorphism
s). One of his best-known results states that the group of Hamiltonian diffeomorphisms of a compact
, connected
, symplectic manifold
is a simple group
; in particular, it does not admit any non-trivial homomorphism
to the real line.
Banyaga is an editor of Afrika Matematica, the journal of the African Mathematical Union
, and an editor of the African Journal of Mathematics. He has supervised the theses of 7 Ph.D. students.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
n mathematician
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....
whose research fields include symplectic topology
Symplectic topology
Symplectic geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form...
and contact geometry
Contact geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle and specified by a one-form, both of which satisfy a 'maximum non-degeneracy' condition called 'complete non-integrability'...
. He is currently a Professor of Mathematics at Pennsylvania State University
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
.
Biography
Banyaga earned 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...
degree in 1976 at the University of Geneva
University of Geneva
The University of Geneva is a public research university located in Geneva, Switzerland.It was founded in 1559 by John Calvin, as a theological seminary and law school. It remained focused on theology until the 17th century, when it became a center for Enlightenment scholarship. In 1873, it...
under the supervision of André Haefliger
André Haefliger
André Haefliger is a Swiss mathematician who works primarily on topology.He studied mathematics in Lausanne. He received his PhD in 1958 from the University of Strasbourg under the supervision of Charles Ehresmann with "Structures feuilletées et cohomologie à valeurs dans un faisceau de...
. He was a member of the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
(1977–1978), Benjamin Peirce
Benjamin Peirce
Benjamin Peirce was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philosophy of mathematics....
Assistant Professor at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
(1978–1982), and Assistant Professor at Boston University
Boston University
Boston University is a private research university located in Boston, Massachusetts. With more than 4,000 faculty members and more than 31,000 students, Boston University is one of the largest private universities in the United States and one of Boston's largest employers...
(1982–1984), before joining the faculty at Pennsylvania State University in 1984 as Associate Professor. He was promoted to Full Professor in 1992.
He has made significant contributions in symplectic topology, especially on the structure of groups
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...
of diffeomorphism
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth.- Definition :...
s preserving a symplectic form (symplectomorphism
Symplectomorphism
In mathematics, a symplectomorphism is an isomorphism in the category of symplectic manifolds.-Formal definition:A diffeomorphism between two symplectic manifolds f: \rightarrow is called symplectomorphism, iff^*\omega'=\omega,...
s). One of his best-known results states that the group of Hamiltonian diffeomorphisms of a compact
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
, connected
Connectedness
In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected...
, symplectic manifold
Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology...
is a simple group
Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated...
; in particular, it does not admit any non-trivial homomorphism
Homomorphism
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
to the real line.
Banyaga is an editor of Afrika Matematica, the journal of the African Mathematical Union
African Mathematical Union
The African Mathematical Union or Union Mathematique Africaine is an African organization dedicated to the development of mathematics in Africa. It was founded in 1976 in Rabat, Morocco, during the first Pan-African Congress of Mathematicians with Henri Hogbe Nlend as its first President...
, and an editor of the African Journal of Mathematics. He has supervised the theses of 7 Ph.D. students.
Articles
- A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Commentarii Mathematici HelveticiCommentarii Mathematici HelveticiThe Commentarii Mathematici Helvetici is a scholarly journal in mathematics published by the European Mathematical Society. The Swiss Mathematical Society started the journal in 1929 after a meeting in May of the previous year. The scope of the journal includes research articles in all aspects in...
53 (1978), no. 2, 174–227. - A. Banyaga, On fixed points of symplectic maps, Inventiones MathematicaeInventiones MathematicaeInventiones Mathematicae, often just referred to as Inventiones, is a mathematical journal published monthly by Springer Verlag. It was founded in 1966.-Editors:...
56 (1980), no. 3, 215–229. - A. Banyaga, On Isomorphic Classical Diffeomorphism Groups. I., Proceedings of the American Mathematical SocietyProceedings of the American Mathematical SocietyProceedings of the American Mathematical Society is a monthly mathematics journal published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages....
98 (1986), no. 1, 113–118. - A. Banyaga, On Isomorphic Classical Diffeomorphism Groups. II., Journal of Differential GeometryJournal of Differential GeometryThe Journal of Differential Geometry is a peer-reviewed mathematical journal published by the Lehigh University. The journal publishes nine issues per year and is distributed by International Press. Surveys in Differential Geometry] It also publishes an annual supplement in book form called...
28 (1988), no. 1, 23–35. - A. Banyaga, A note on WeinsteinAlan WeinsteinAlan David Weinstein is a professor of mathematics at the University of California, Berkeley who works in symplectic geometry, Poisson Geometry and Mathematical Physics....
's conjecture, Proceedings of the American Mathematical Society 123 (1995), no. 12, 3901–3906.
External links
- Home page at PSU
- Vita
- Augustin Banyaga, at Mathematicians of the filipinong mga taNGA at bobo