Lowell Edwin Jones (born 1945) is an American professor of mathematics at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...

. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with

F. Thomas Farrell Francis Thomas Farrell (born November 14, 1941, in Ohio, United States) is an American mathematician who has made contributions in the area of topology and differential geometry. Farrell is a distinguished professor emeritus of mathematics at Bin ...

on the Farrell-Jones conjecture.

Education and career

Jones received his

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

from

Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

in 1970 under the guidance of

Wu-Chung Hsiang Wu-Chung Hsiang (; born 12 June 1935) is a Taiwanese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential Topolog ...

. Jones' dissertation topic, assigned by Hsiang, concerned the fixed-point theorem of

Paul Althaus Smith Paul Althaus Smith (May 18, 1900June 13, 1980) was an American mathematician. His name occurs in two significant conjectures in geometric topology: the Smith conjecture, which is now a theorem, and the Hilbert–Smith conjecture, which was proved ...

. Jones joined Stony Brook University in 1975.

Mathematical contributions

When Farrell and Jones first started collaborating they gave the very first example of an

Anosov diffeomorphism In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold ''M'' is a certain type of mapping, from ''M'' to itself, with rather clearly marked local directions of "expansion" and "contr ...

on a manifold which was not infranil. Later, Jones and Farrell, also a student of Hsiang, caused a paradigm shift in higher dimensional topology when they applied ideas from differential geometry, and dynamics to questions such as the

Borel conjecture In geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of ...

. The Farrell-Jones conjecture implies the Borel Conjecture for manifolds of dimension greater than four. Jones, and Farrell published about fifty papers during their 25-year collaboration. Jones was invited to speak at the 1990

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Kyoto Kyoto ( or ; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it t ...

References

1945 births Living people Stony Brook University faculty Yale University alumni People from Port Jefferson, New York Mathematicians from New York (state) 20th-century American mathematicians American topologists American geometers {{US-mathematician-stub