John Roe (mathematician)
John Roe ( born October 6, 1959) is a British mathematician.
Roe grew up in rural Shropshire. He went to Rugby School, studied at Cambridge University and in 1985 with Michael Atiyah at the University of Oxford doctorate (Analysis on manifolds ). As a post - graduate student he was at the Mathematical Sciences Research Institute ( MSRI ) in Berkeley, and then a tutor at Jesus College, Oxford. Since 1998 he is professor at the Pennsylvania State University.
He has been working for his dissertation index theory ( in the environment of the Atiyah-Singer index theorem and its generalizations ). He dealt with Coarse Geometry (literally Coarse geometry) with applications to the definition of the index of elliptic operators on non-compact manifolds ( where the index not be an integer greater needs but item an index group in the context of K-theory of operator algebras ) and the appropriate generalization of the Atiyah-Singer index theorem. He also dealt with applications of this theory to the Novikov conjecture in differential topology.
It also deals with noncommutative geometry and is co-editor of the Journal of Noncommutative Geometry.
In 1996 he was awarded the Whitehead Prize. He is a Fellow of the American Mathematical Society.
He has been married since 1986 and has two children.
Writings
- Elementary Geometry, Oxford University Press 1993
- Coarse cohomology and index theory on complete Riemannian manifolds, American Mathematical Society 1993
- Publisher: Index theory, coarse geometry and topology of manifolds, American Mathematical Society 1996
- Nigel Higson: Analytic K- homology, Oxford University Press 2000
- Nigel Higson (Editor): Surveys in Noncommutative Geometry, American Mathematical Society 2006 ( Inst Clay Math Symp )
- Elliptic operators, topology, and asymptotic methods, Wiley 1988
- Lectures on coarse geometry, American Mathematical Society 2003
- Conjecture Amenable group actions and the Novikov: Nigel Higson. J. Reine Angew. Math 519 (2000), 143-153.