J. Peter May
Encyclopedia
Jon Peter May is an American
mathematician
, working in the fields of algebraic topology
, category theory
, homotopy theory, and the foundational aspects of spectra
. He is known, in particular, for inventing the term operads
and the May spectral sequence
.
He received a B.A.
from Swarthmore College
in 1960, and a Ph.D.
from Princeton University
in 1964. His thesis, written under the direction of John Moore
, was titled The cohomology
of restricted Lie algebra
s and of Hopf algebra
s: Application to the Steenrod algebra
. From 1964 to 1967 he taught at Yale University
. He has been a faculty member at the University of Chicago
since 1967, and a Professor since 1970.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, working in the fields of algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which 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.Although algebraic topology...
, category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, homotopy theory, and the foundational aspects of spectra
Spectrum (homotopy theory)
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, any of which gives a context for the same stable homotopy theory....
. He is known, in particular, for inventing the term operads
Operad theory
Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity. Operads generalize the various associativity properties already observed in algebras and coalgebras such as...
and the May spectral sequence
May spectral sequence
In mathematics, the May spectral sequence is a spectral sequence, introduced by , used for calculating the initial term of the Adams spectral sequence, which is in turn used for calculating the stable homotopy groups of spheres. It is described in detail in ....
.
He received a B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
from Swarthmore College
Swarthmore College
Swarthmore College is a private, independent, liberal arts college in the United States with an enrollment of about 1,500 students. The college is located in the borough of Swarthmore, Pennsylvania, 11 miles southwest of Philadelphia....
in 1960, and a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1964. His thesis, written under the direction of John Moore
John Coleman Moore
John Coleman Moore is an American mathematician. He received his Ph.D. in 1952 from Brown University under the supervision of George W. Whitehead. His most heavily cited paper is on Hopf algebras, co-authored with John Milnor. As a faculty member at Princeton University, he advised 23 students and...
, was titled The cohomology
Cohomology
In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries...
of restricted Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s and of Hopf algebra
Hopf algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an algebra and a coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.Hopf algebras occur naturally...
s: Application to the Steenrod algebra
Steenrod algebra
In algebraic topology, a Steenrod algebra was defined by to be the algebra of stable cohomology operations for mod p cohomology.For a given prime number p, the Steenrod algebra Ap is the graded Hopf algebra over the field Fp of order p, consisting of all stable cohomology operations for mod p...
. From 1964 to 1967 he taught at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
. He has been a faculty member at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
since 1967, and a Professor since 1970.