Jack Morava
Encyclopedia
Jack Johnson Morava is an American topologist.
Of Czech
and Appalachian
descent, he was raised in Mercedes, Texas
(essentially, in northern Tamaulipas
); an early interest in topology
was strongly encouraged by his parents. He enrolled at Rice University
in 1962 as a physics major, but (with the help of Jim Douglas) entered the graduate mathematics program in 1964, receiving a Ph.D. in 1968.
His thesis adviser was Morton L. Curtis. He subsequently spent a year at Oxford and the Princeton Institute for Advanced Study, where he was mentored by Eldon Dyer and Michael Atiyah
.
Following a suggestion of the latter, he specialized in relations between K-theory
and cobordism
, and when Quillen's work on cobordism appeared, he applied it, together with work of Sergei Novikov
and Dennis Sullivan
, to stable homotopy theory
.
In particular, he focused attention on certain ring-spectra parametrized by one-dimensional
formal group laws over a field, which generalize classical topological K-theory. From a modern point of view [i.e., since Hopkins
, Smith, and Devinatz's proof of Ravenel's nilpotence conjecture] it is natural to think of these cohomology theories as the geometric points associated to the prime ideals of the stable homotopy category. Their multiplicative automorphism groups are essentially the groups of units in certain p-adic division algebras, and thus have interesting connections to local class field theory
.
In 1970 he and the linguistic anthropologist Ellen Lee Contini
married; they have two children,
Aili and Michael. They spent a year at the Steklov
Institute in Moscow on a US National Academy of Sciences fellowship, where he was influenced by contact with I. M. Gel’fand
, Yuri
Manin and Sergei Novikov. He joined the Johns Hopkins University faculty in 1980, where he was later involved in organizing the Japan-US Mathematics Institute. Much of his more recent work involves the application of cobordism categories to mathematical physics, and is posted on the ArXiv
; from 2006 to 2010 he was active in DARPA's fundamental questions of biology
http://www.darpa.mil/dso/thrusts/math/funmath/fundamental/index.htm initiative.
Of Czech
Tábor
Tábor is a city of the Czech Republic, in the South Bohemian Region. It is named after Mount Tabor, which is believed by many to be the place of the Transfiguration of Christ; however, the name became popular and nowadays translates to "camp" or "encampment" in the Czech language.The town was...
and Appalachian
Bob Benge
Bob Benge , also known as "Captain Benge" or "The Bench" to frontiersmen, was one of the most feared Cherokee leaders on the frontier during the Chickamauga wars.-Early life:...
descent, he was raised in Mercedes, Texas
Mercedes, Texas
Mercedes is a city in Hidalgo County, Texas, United States. The population was 15,570 at the 2010 census. It is part of the McAllen–Edinburg–Mission and Reynosa–McAllen metropolitan areas.-Geography:Mercedes is located at ....
(essentially, in northern Tamaulipas
Tamaulipas
Tamaulipas officially Estado Libre y Soberano de Tamaulipas is one of the 31 states which, with the Federal District, comprise the 32 Federal Entities of Mexico. It is divided in 43 municipalities and its capital city is Ciudad Victoria. The capital city was named after Guadalupe Victoria, the...
); an early interest in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
was strongly encouraged by his parents. He enrolled at Rice University
Rice University
William Marsh Rice University, commonly referred to as Rice University or Rice, is a private research university located on a heavily wooded campus in Houston, Texas, United States...
in 1962 as a physics major, but (with the help of Jim Douglas) entered the graduate mathematics program in 1964, receiving a Ph.D. in 1968.
His thesis adviser was Morton L. Curtis. He subsequently spent a year at Oxford and the Princeton Institute for Advanced Study, where he was mentored by Eldon Dyer and Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
.
Following a suggestion of the latter, he specialized in relations between K-theory
K-theory
In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
and cobordism
Cobordism
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 are cobordant if their disjoint union is the boundary of a manifold one dimension higher. The name comes...
, and when Quillen's work on cobordism appeared, he applied it, together with work of Sergei Novikov
Sergei Novikov
Sergey Novikov may refer to:*Sergei Borisovich Novikov , Soviet Russian footballer*Sergei Novikov , Russian mathematician*Sergey Novikov , Belarussian biathlete...
and Dennis Sullivan
Dennis Sullivan
Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.-Work in topology:He...
, to stable homotopy theory
Stable homotopy theory
In mathematics, stable homotopy theory is that part of homotopy theory concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor...
.
In particular, he focused attention on certain ring-spectra parametrized by one-dimensional
formal group laws over a field, which generalize classical topological K-theory. From a modern point of view [i.e., since Hopkins
Michael J. Hopkins
Michael Jerome Hopkins is an American mathematician known for work in algebraic topology.-Life:He received his Ph.D. from Northwestern University in 1984 under the direction of Mark Mahowald. In 1984 he also received his D.Phil...
, Smith, and Devinatz's proof of Ravenel's nilpotence conjecture] it is natural to think of these cohomology theories as the geometric points associated to the prime ideals of the stable homotopy category. Their multiplicative automorphism groups are essentially the groups of units in certain p-adic division algebras, and thus have interesting connections to local class field theory
Class field theory
In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields.Most of the central results in this area were proved in the period between 1900 and 1950...
.
In 1970 he and the linguistic anthropologist Ellen Lee Contini
Ellen Contini-Morava
Ellen Contini-Morava is an anthropological linguist at the University of Virginia College of Arts & Sciences, interested in cognitive linguistics issues, Discourse analysis, and classification ; in particular, in systems between lexicon and grammar in size...
married; they have two children,
Aili and Michael. They spent a year at the Steklov
Steklov Institute of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute is a research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. It was established April 24, 1934 by the decision of the General Assembly of the Academy of Sciences of the USSR in...
Institute in Moscow on a US National Academy of Sciences fellowship, where he was influenced by contact with I. M. Gel’fand
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a Soviet mathematician who made major contributions to many branches of mathematics, including group theory, representation theory and functional analysis...
, Yuri
Yuri I. Manin
Yuri Ivanovitch Manin is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.-Biography:...
Manin and Sergei Novikov. He joined the Johns Hopkins University faculty in 1980, where he was later involved in organizing the Japan-US Mathematics Institute. Much of his more recent work involves the application of cobordism categories to mathematical physics, and is posted on the ArXiv
ArXiv
The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...
; from 2006 to 2010 he was active in DARPA's fundamental questions of biology
http://www.darpa.mil/dso/thrusts/math/funmath/fundamental/index.htm initiative.