Victor William Guillemin (born 1937 in

Boston Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeas ...

) is an American

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, mathematical structure, structure, space, Mathematica ...

. He works at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

in the field of

symplectic geometry 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 ...

, and he has also made contributions to the fields of microlocal analysis,

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operator (mathematics), operators in a variety of mathematical ...

, and

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

Education and career

Guillemin obtained a B.A. at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

in 1959, as well as an M. A. at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

in 1960. He received a Ph.D. in mathematics from Harvard University in 1962; his dissertation, entitled ''Theory of Finite G-Structures,'' was written under the direction of

Shlomo Sternberg Shlomo Zvi Sternberg (January 20, 1936 – August 23, 2024) was an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. He also wrote some well-known textbooks. Education and career Sternber ...

. He worked at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

from 1963 to 1966 and then moved to the

as assistant professor. He became associate professor in 1969 and full professor in 1973.

Awards and honors

Guillemin was awarded in 1969 a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

, in 1988 a

Guggenheim fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

and in 1996 a Humboldt fellowship. In 1970 he was invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Nice. He was elected a fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1984 and of the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

in 1985. In 2003, he was awarded the Leroy P. Steele Prize for Lifetime Achievement by the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2012 he became a fellow of the

Research

Guillemin worked in several areas in analysis and geometry, including microlocal analysis, symplectic

group actions In mathematics, a group action of a group G on a set S is a group homomorphism from G to some group (under function composition) of functions from S to itself. It is said that G acts on S. Many sets of transformations form a group under funct ...

, and

of elliptic operators on

manifolds In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

. He is the author or co-author of numerous books and monographs, including a widely used textbook on

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

, written jointly with Alan Pollack in 1974, and a monograph on symplectic geometry in physics, written jointly with Shlomo Sternberg in 1986.

Family

Victor Guillemins's uncle

Ernst Guillemin Ernst Adolph Guillemin (May 8, 1898 – April 1, 1970) was an American electrical engineer and computer scientist at the Massachusetts Institute of Technology who spent his career extending the art and science of linear network analysis and synth ...

was a Professor of Electrical Engineering and Computer Science at MIT, his younger brother Robert Charles Guillemin was a sidewalk artist, his brother-in-law Ray Raphael is an historian, and his daughter Karen Guillemin is a Professor of Biology at the

University of Oregon The University of Oregon (UO, U of O or Oregon) is a Public university, public research university in Eugene, Oregon, United States. Founded in 1876, the university is organized into nine colleges and schools and offers 420 undergraduate and gra ...

Selected publications

* * *; reprinted in 1990 as a
on-line book
* * *

References

External links

* *Victor Guillemin'
personal web page
{{DEFAULTSORT:Guillemin, Victor Members of the United States National Academy of Sciences 20th-century American mathematicians 21st-century American mathematicians Differential geometers American topologists Massachusetts Institute of Technology School of Science faculty Harvard College alumni University of Chicago alumni Fellows of the American Mathematical Society Living people 1937 births Harvard Graduate School of Arts and Sciences alumni Sloan Research Fellows