Augustin Banyaga (born March 31, 1947) is a

Rwanda Rwanda (; rw, u Rwanda ), officially the Republic of Rwanda, is a landlocked country in the Great Rift Valley of Central Africa, where the African Great Lakes region and Southeast Africa converge. Located a few degrees south of the Equator ...

n-born

America The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

whose research fields include

symplectic topology Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the H ...

and

contact geometry In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution (differential geometry), distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. ...

. He is currently a Professor of Mathematics at

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsylvan ...

Biography

He earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

degree in 1976 at the

University of Geneva The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centu ...

under the supervision of

André Haefliger André Haefliger (born 22 May 1929 in Nyon, Switzerland) is a Swiss mathematician who works primarily on topology. Education and career Haefliger went to school in Nyon and then attended his final years at Collège Calvin in Geneva. He studied ...

. (Banyaga was the first person from Rwanda to obtain a Ph.D. in mathematics.) He was a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

(1977–1978),

Benjamin Peirce Benjamin Peirce (; April 4, 1809 – October 6, 1880) 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 philoso ...

Assistant Professor at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

(1978–1982), and assistant professor at

Boston University Boston University (BU) is a private research university in Boston, Massachusetts. The university is nonsectarian, but has a historical affiliation with the United Methodist Church. It was founded in 1839 by Methodists with its original campu ...

(1982–1984), before joining the faculty at Pennsylvania State University in 1984 as associate professor. He was promoted to full professor in 1992. In 2009 Banyaga was elected a Fellow of the

African Academy of Sciences The African Academy of Sciences (AAS) is a non-aligned, non-political, not-for-profit, pan-African learned society formed in 1985. The AAS elects fellows ( FAAS) and affiliates. The AAS also awards the Obasanjo Prize for Scientific Discovery and ...

, and in 2015 he was named a Distinguished Senior Scholar by

. He has made significant contributions in symplectic topology, especially on the structure of

groups A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

diffeomorphism In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two m ...

s preserving a symplectic form (

symplectomorphism In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the sy ...

s). One of his best-known results states that the group of Hamiltonian diffeomorphisms of a

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

connected Connected may refer to: Film and television * ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular'' * '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film * ''Connected'' (2015 TV ...

, symplectic manifold is a

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

; in particular, it does not admit any non-trivial

homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" ...

to the real line. Banyaga is an editor of '' Afrika Matematica'', the journal of the

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 ...

, and an editor of the '' African Journal of Mathematics''. He has supervised the theses of 9 Ph.D. students.

Bibliography

;Articles * Augustin Banyaga, ''Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique'',

Commentarii Mathematici Helvetici The ''Commentarii Mathematici Helvetici'' is a quarterly peer-reviewed scientific journal in mathematics. The Swiss Mathematical Society started the journal in 1929 after a meeting in May of the previous year. The Swiss Mathematical Society sti ...

53 (1978), no. 2, 174–227. * Augustin Banyaga, ''On fixed points of symplectic maps'',

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors ...

56 (1980), no. 3, 215–229. * Augustin Banyaga, ''On Isomorphic Classical Diffeomorphism Groups. I.'',

Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ' ...

98 (1986), no. 1, 113–118. * Augustin Banyaga, ''On Isomorphic Classical Diffeomorphism Groups. II.'',

Journal of Differential Geometry The ''Journal of Differential Geometry'' is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in b ...

28 (1988), no. 1, 23–35. * Augustin Banyaga, ''A note on

Weinstein Weinstein is a German or Yiddish surname meaning wine stone, referring to the crystals of cream of tartar (potassium bitartrate) resulting from the process of fermenting grape juice.Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ' ...

123 (1990), no. 12, 3901–3906. ;Books * *

References

External links

* * * {{DEFAULTSORT:Banyaga, Augustin People from Kigali 20th-century American mathematicians 21st-century American mathematicians Topologists Pennsylvania State University faculty Harvard University faculty Boston University faculty Institute for Advanced Study visiting scholars Living people 1947 births Rwandan emigrants to the United States University of Geneva alumni Fellows of the African Academy of Sciences