# Peter Landweber

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**Peter Steven Landweber** (born August 17, 1940, in Washington D. C.)[1] is an American mathematician working in [algebraic topology](/source/Algebraic_topology).

Landweber studied at the [University of Iowa](/source/University_of_Iowa) (B.S. 1960) and [Harvard University](/source/Harvard_University) (master's degree 1961), where he graduated in 1965 after studying under [Raoul Bott](/source/Raoul_Bott) ([Künneth formulas](/source/K%C3%BCnneth_theorem) for [bordism](/source/Cobordism) theories).[2] He was then Assistant Professor at the [University of Virginia](/source/University_of_Virginia) (from 1965) and at [Yale University](/source/Yale_University) from 1968 to 1970. From 1967 to 1968 he was at the [Institute for Advanced Study](/source/Institute_for_Advanced_Study) in Princeton, [New Jersey](/source/New_Jersey). In 1970, he became [Associate Professor](/source/Associate_professor) at [Rutgers University](/source/Rutgers_University), where he taught from 1974 until his retirement in 2007. From 1974 to 1975 he was a NATO fellow at the [University of Cambridge](/source/University_of_Cambridge). Since 2007, he is a Professor Emeritus at Rutgers University.[3]

Landweber studied [complex bordism](/source/Complex_bordism) in algebraic topology (introducing [Landweber–Novikov algebra](/source/Landweber%E2%80%93Novikov_algebra) in the 1960s[4]). In the beginning of the 1970s, he proved his [exact functor theorem](/source/Exact_functor_theorem), which allows the construction of a [homology theory](/source/Homology_theory) from a [formal group law](/source/Formal_group_law).[5] In 1986 he introduced [elliptic cohomology](/source/Elliptic_cohomology) with [Douglas C. Ravenel](/source/Douglas_C._Ravenel) and [Robert E. Stong](/source/Robert_E._Stong), which is a [generalized cohomology theory](/source/Generalized_cohomology_theory) with applications to [modular forms](/source/Modular_form) and [elliptic curves](/source/Elliptic_curve).[6] From 1989 to 1992 he was Chairman of the Russian translation Committee of the [American Mathematical Society](/source/American_Mathematical_Society). He is also a fellow of the society.[7]

Peter Landweber is the elder son of the engineer [Louis Landweber](/source/Louis_Landweber) and the father of the molecular biologist [Laura Faye Landweber](/source/Laura_Landweber)[8] (born 1967) and of the mathematician Gregory David Landweber[9] (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

1. *American Men and Women of Science*, Thomson Gale 2004

1. [of the Rutgers University, after his retirement in 2007](http://www.math.rutgers.edu/newsletter/newsletter2007.htmlNewsletter), and American Men and Women of Science]

1. Landweber, Cobordism operations and Hopf algebras, [Transactions of the AMS](/source/Transactions_of_the_AMS), issue 129, 1967, pg. 94–110 [doi:10.2307/1994365](https://doi.org/10.2307/1994365). [Sergei Petrowitsch Nowikow](/source/Sergei_Petrowitsch_Nowikow) *The methods of algebraic topology from the viewpoint of cobordism theory*, Math. USSR Izvestija, issue 1, 1967, pg.827

1. Landweber *Homological properties of comodules over MU*(MU) and BP*(BP)*, [American Journal of Mathematics](/source/American_Journal_of_Mathematics), issue 98, 1976, pg. 591–610 [doi:10.2307/2373808](https://doi.org/10.2307/2373808)

1. Landweber, LN Mathematics 1326, 1988 and Landweber, Ravenel, Stong *Periodic cohomology theories defined by elliptic curves*, Contemporary Mathematics, issue 181, 1995 (Čech Centennial, Boston 1993). Known as the Landweber–Ravenel–Stong theory. It uses the exact functor theorem.

1. [List of Fellows of the American Mathematical Society](http://www.ams.org/profession/fellows-list) [Archived](https://web.archive.org/web/20180825194636/http://www.ams.org/profession/fellows-list) 2018-08-25 at the Wayback Machine, retrieved 2013-11-16.

1. [Laura Landweber, Columbia University, Biological Sciences](http://biology.columbia.edu/people/landweber)

## External links

- [Haynes Miller](/source/Haynes_Miller): [*A marriage of manifolds and algebra: The mathematical work of Peter Landweber*](https://web.archive.org/web/20160824183827/http://math.bard.edu/greg/landweber.pdf)
- [Web page on his 60th birthday](http://www.kaleidoscope.net/cobordism/)

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