Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. Landweber studied at the

University of Iowa The University of Iowa (UI, U of I, UIowa, or simply Iowa) is a public university, public research university in Iowa City, Iowa, United States. Founded in 1847, it is the oldest and largest university in the state. The University of Iowa is org ...

(B.SC. 1960) and the

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 ...

(master's degree 1961), where he graduated in 1965 after studying under

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...

(Künneth formulas for bordism theories). He was then Assistant Professor at the

University of Virginia The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United S ...

(from 1965) and at

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

from 1968 to 1970. From 1967 to 1968 he was at 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 ...

in Princeton,

New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, southeast, and south by the Atlantic Ocean; on the west by the Delaware ...

. In 1970, he became

Associate Professor Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''. Overview In the ''North American system'', used in the United States and many other countries, it is a ...

at the

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

, where he taught from 1974 until his retirement in 2007. From 1974 to 1975 he was a NATO fellow at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. Since 2007, he is a Professor Emeritus at Rutgers University. Landweber studied

complex bordism In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its Spectrum (homotopy theory), spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, s ...

in algebraic topology (introducing Landweber–Novikov algebra in the 1960s). In the beginning of the 1970s, he proved his

exact functor theorem In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation of a homology theory leads to a formal group law. The Landweber exact functor theorem (or ...

, which allows the construction of a homology theory from a

formal group law In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one ...

. In 1986 he introduced

elliptic cohomology In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms. History and motivation Historically, elliptic cohomology arose from the study of elliptic genera. I ...

with Douglas C. Ravenel and Robert E. Stong, which is a

generalized cohomology theory In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...

with applications to

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

s and

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s. From 1989 to 1992 he was Chairman of the Russian translation Committee of the American Mathematical Society. He is also a fellow of the society. Peter Landweber is the elder son of the engineer

Louis Landweber Louis Landweber (8 January 1912, New York City – 19 January 1998, Iowa City, Iowa), was a leading ship hydrodynamicist, known for Landweber iteration. Education and career Landweber received in 1932 a bachelor's degree in mathematics from the C ...

and the father of the molecular biologist Laura Faye Landweber (born 1967) and of the mathematician Gregory David Landweber (born 1971).

Selected publications

*(Ed.): elliptic curves and modular forms in algebraic topology (= lecture notes in mathematics. ) issue 1326). Springer 1988 (proceedings of a Conference at the Institute for Advanced Study in 1986). Landweber: other elliptic and modular forms. PP. 55–86; Elliptic genera-of introductory overview. pg. 1–10.

References

External links

* Haynes Miller
''A marriage of manifolds and algebra: The mathematical work of Peter Landweber''

Web page on his 60th birthday
{{DEFAULTSORT:Landweber, Peter Steven 1940 births Living people 20th-century American mathematicians 21st-century American mathematicians University of Iowa alumni Harvard University alumni University of Virginia faculty Yale University faculty Rutgers University faculty Fellows of the American Mathematical Society Mathematicians from Washington, D.C. Topologists