Peter Landweber

Last updated

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

Contents

Landweber studied at the University of Iowa (B.SC. 1960) and Harvard University (master's degree 1961), where he graduated in 1965 after studying under Raoul Bott (Künneth formulas for bordism theories). [2] He was then Assistant Professor at the University of Virginia (from 1965) and at Yale University from 1968 to 1970. From 1967 to 1968 he was at the Institute for Advanced Study in Princeton, New Jersey. In 1970, he became Associate Professor at 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. Since 2007, he is a Professor Emeritus at Rutgers University. [3]

Landweber studied complex bordism in algebraic topology (introducing Landweber–Novikov algebra in the 1960s [4] ). In the beginning of the 1970s, he proved his exact functor theorem, which allows the construction of a homology theory from a formal group law. [5] In 1986 he introduced elliptic cohomology with Douglas C. Ravenel and Robert E. Stong, which is a generalized cohomology theory with applications to modular forms and elliptic curves. [6] 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. [7]

Peter Landweber is the elder son of the engineer Louis Landweber and the father of the molecular biologist Laura Faye Landweber [8] (born 1967) and of the mathematician Gregory David Landweber [9] (born 1971).

Selected publications

Related Research Articles

<span class="mw-page-title-main">Michael Atiyah</span> British-Lebanese mathematician (1929–2019)

Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.

<span class="mw-page-title-main">Algebraic topology</span> Branch of mathematics

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.

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 as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.

<span class="mw-page-title-main">Cobordism</span>

In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher.

In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry. This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.

In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are easier to compute.

In mathematics, the Thom space,Thom complex, or Pontryagin–Thom construction of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.

<span class="mw-page-title-main">Arithmetic geometry</span> Branch of algebraic geometry focused on problems in number theory

In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.

In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space S of a family of algebraic varieties . The fibers of the vector bundle are the de Rham cohomology groups of the fibers of the family. It was introduced by Yuri Manin (1958) for curves S and by Alexander Grothendieck (1966) in higher dimensions.

In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory. In concrete terms, for any integer n there is a topological space , and these spaces are equipped with certain maps between them, so that for any topological space X, one obtains an abelian group structure on the set of homotopy classes of continuous maps from X to . One feature that distinguishes tmf is the fact that its coefficient ring, (point), is almost the same as the graded ring of holomorphic modular forms with integral cusp expansions. Indeed, these two rings become isomorphic after inverting the primes 2 and 3, but this inversion erases a lot of torsion information in the coefficient ring.

In mathematics, elliptic cohomology is a cohomology theory in the sense of algebraic topology. It is related to elliptic curves and modular forms.

In mathematics, Brown–Peterson cohomology is a generalized cohomology theory introduced by Edgar H. Brown and Franklin P. Peterson (1966), depending on a choice of prime p. It is described in detail by Douglas Ravenel . Its representing spectrum is denoted by BP.

In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain.

<span class="mw-page-title-main">Michael J. Hopkins</span> American mathematician

Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.

<span class="mw-page-title-main">Douglas Ravenel</span> American mathematician

Douglas Conner Ravenel is an American mathematician known for work in algebraic topology.

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 can be seen as a method to reverse this process: it constructs a homology theory out of a formal group law.

In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic" point of view, which is based on Quillen's work relating cohomology theories to formal groups. In this picture, theories are classified in terms of their "chromatic levels"; i.e., the heights of the formal groups that define the theories via the Landweber exact functor theorem. Typical theories it studies include: complex K-theory, elliptic cohomology, Morava K-theory and tmf.

References

  1. ↑ American Men and Women of Science, Thomson Gale 2004
  2. ↑ Peter Steven Landweber at the Mathematics Genealogy Project
  3. ↑ of the Rutgers University, after his retirement in 2007, and American Men and Women of Science]
  4. ↑ Landweber, Cobordism operations and Hopf algebras, Transactions of the AMS, issue 129, 1967, pg. 94–110 doi : 10.2307/1994365. Sergei Petrowitsch Nowikow The methods of algebraic topology from the viewpoint of cobordism theory, Math. USSR Izvestija, issue 1, 1967, pg.827
  5. ↑ Landweber Homological properties of comodules over MU*(MU) and BP*(BP), American Journal of Mathematics, issue 98, 1976, pg. 591–610 doi : 10.2307/2373808
  6. ↑ 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.
  7. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-11-16.
  8. ↑ Laura Landweber, Columbia University, Biological Sciences
  9. ↑ Gergory D. Landweber at the Mathematics Genealogy Project
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.