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| workplaces = [[Stony Brook University]]
| workplaces = [[Stony Brook University]]
| alma_mater = [[Yale University]]
| alma_mater = [[Yale University]]
| doctoral_advisor = [https://www.math.princeton.edu/directory/wu-chung-hsiang Wu Chang Hsiang]
| doctoral_advisor = [[Wu-Chung Hsiang]]
| academic_advisors =
| academic_advisors =
| doctoral_students =
| doctoral_students =
| notable_students =
| notable_students =
| known_for = Farrell–Jones conjecture
| known_for = [[Farrell–Jones conjecture]]
| author_abbrev_bot =
| author_abbrev_bot =
| author_abbrev_zoo =
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'''Lowell Jones''' (born 1945) is an American professor of mathematics at [[Stony Brook University]]<ref>{{cite web|title=Stony Brook Faculty page|url=http://www.math.stonybrook.edu/cards/joneslowell.html|accessdate=20 December 2015}}</ref>. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with [[F. Thomas Farrell]] on the [[Farrell–Jones conjecture|Farrell-Jones conjecture]].
'''Lowell Jones''' (born 1945) is an American professor of mathematics at [[Stony Brook University]]<ref>{{cite web|title=Stony Brook Faculty page|url=http://www.math.stonybrook.edu/cards/joneslowell.html|accessdate=20 December 2015}}</ref>. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with [[F. Thomas Farrell]] on the [[Farrell–Jones conjecture]].


==Education and career==
==Education and career==
Jones received his Ph.D. from [[Yale University]] in 1970 under the guidance of Wu-Chung Hsiang.<ref>{{cite web|title=Mathematics Genealogy Project|url=http://genealogy.math.ndsu.nodak.edu/id.php?id=8429|publisher=Department of Mathematics North Dakota State University|accessdate=20 December 2015}}</ref> Jones' dissertation topic, assigned by Hsiang,<ref>{{Cite journal|jstor=1970734|doi=10.1090/S0002-9904-1972-12934-3 |url=http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12934-3/S0002-9904-1972-12934-3.pdf|title=The converse to the fixed point theorem of P. A. Smith |journal=Bulletin of the American Mathematical Society |volume=78 |issue=2 |pages=234 |year=1972 |last1=Jones |first1=Lowell }}</ref> concerned the fixed-point theorem.
Jones received his [[Ph.D.]] from [[Yale University]] in 1970 under the guidance of [[Wu-Chung Hsiang]].<ref>{{cite web|title=Mathematics Genealogy Project|url=http://genealogy.math.ndsu.nodak.edu/id.php?id=8429|publisher=Department of Mathematics North Dakota State University|accessdate=20 December 2015}}</ref> Jones' dissertation topic, assigned by Hsiang,<ref>{{Cite journal|jstor=1970734|doi=10.1090/S0002-9904-1972-12934-3 |url=http://www.ams.org/journals/bull/1972-78-02/S0002-9904-1972-12934-3/S0002-9904-1972-12934-3.pdf|title=The converse to the fixed point theorem of P. A. Smith |journal=[[Bulletin of the American Mathematical Society]] |volume=78 |issue=2 |pages=234 |year=1972 |last1=Jones |first1=Lowell }}</ref> concerned the fixed-point theorem.


Jones joined the Stony Brook University in 1975.
Jones joined the Stony Brook University in 1975.


==Mathematical contributions==
==Mathematical contributions==
When Farrell, and Jones first started collaborating they gave the very first example of an Anosov diffeomorphism on a manifold which was not infranil.<ref>{{cite journal|last1=Farrell|first1=F.T.|last2=Jones|first2=L.E.|title=Anosov diffeomorphisms constructed from π1 Diff (Sn)|journal=Topology|date=1978|volume=17|issue=3|pages=273–282|doi=10.1016/0040-9383(78)90031-9}}</ref> 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]]. The Farrell-Jones conjecture <ref>{{cite journal|last1=Farrell|first1=F.T.|last2=Jones|first2=L.E.|title=Isomorphism Conjectures in Algebraic K-Theory|journal=Journal of the American Mathematical Society|date=Apr 1993|volume=2|issue=6|pages=249–297|doi=10.2307/2152801|jstor=2152801}}</ref> implies the Borel Conjecture for higher dimensional manifolds of dimensions greater than four.
When Farrell and Jones first started collaborating they gave the very first example of an [[Anosov diffeomorphism]] on a manifold which was not [[Glossary of Riemannian and metric geometry#I|infranil]].<ref>{{cite journal|last1=Farrell|first1=F.T.|last2=Jones|first2=L.E.|title=Anosov diffeomorphisms constructed from π1 Diff (Sn)|journal=Topology|date=1978|volume=17|issue=3|pages=273–282|doi=10.1016/0040-9383(78)90031-9}}</ref> 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]]. The Farrell-Jones conjecture <ref>{{cite journal|last1=Farrell|first1=F.T.|last2=Jones|first2=L.E.|title=Isomorphism Conjectures in Algebraic K-Theory|journal=Journal of the American Mathematical Society|date=Apr 1993|volume=2|issue=6|pages=249–297|doi=10.2307/2152801|jstor=2152801}}</ref> implies the Borel Conjecture for higher dimensional manifolds of dimensions greater than four.


Jones, and Farrell published about fifty papers during their 25-year collaboration.<ref>{{cite journal|last1=Davis|first1=James|title=The Work of Tom Farrell and Lowell Jones in Topology and Geometry|journal=Pure and Applied Mathematics Quarterly|date=2012|volume=8|issue=1|pages=1–14|arxiv=1006.1489}}</ref>
Jones, and Farrell published about fifty papers during their 25-year collaboration.<ref>{{cite journal|last1=Davis|first1=James|title=The Work of Tom Farrell and Lowell Jones in Topology and Geometry|journal=Pure and Applied Mathematics Quarterly|date=2012|volume=8|issue=1|pages=1–14|arxiv=1006.1489}}</ref>


Jones was invited to speak at the 1990 [[International Congress of Mathematicians]] in Kyoto.<ref>{{cite web|title=Speakers at the ICM|url=http://www.mathunion.org/db/ICM/Speakers/SortedByCongress.php|accessdate=21 December 2015}}</ref>
Jones was invited to speak at the 1990 [[International Congress of Mathematicians]] in [[Kyoto]].<ref>{{cite web|title=Speakers at the ICM|url=http://www.mathunion.org/db/ICM/Speakers/SortedByCongress.php|accessdate=21 December 2015}}</ref>


==References==
==References==

Revision as of 14:39, 13 February 2018

Lowell E. Jones
Born1945
United States
Alma materYale University
Known forFarrell–Jones conjecture
Scientific career
FieldsGeometry, Topology,
InstitutionsStony Brook University
Doctoral advisorWu-Chung Hsiang

Lowell Jones (born 1945) is an American professor of mathematics at Stony Brook University[1]. Jones' primary fields of interest are topology and geometry. Jones is most well known for his collaboration with F. Thomas Farrell on the Farrell–Jones conjecture.

Education and career

Jones received his Ph.D. from Yale University in 1970 under the guidance of Wu-Chung Hsiang.[2] Jones' dissertation topic, assigned by Hsiang,[3] concerned the fixed-point theorem.

Jones joined the Stony Brook University in 1975.

Mathematical contributions

When Farrell and Jones first started collaborating they gave the very first example of an Anosov diffeomorphism on a manifold which was not infranil.[4] 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. The Farrell-Jones conjecture [5] implies the Borel Conjecture for higher dimensional manifolds of dimensions greater than four.

Jones, and Farrell published about fifty papers during their 25-year collaboration.[6]

Jones was invited to speak at the 1990 International Congress of Mathematicians in Kyoto.[7]

References

  1. ^ "Stony Brook Faculty page". Retrieved 20 December 2015.
  2. ^ "Mathematics Genealogy Project". Department of Mathematics North Dakota State University. Retrieved 20 December 2015.
  3. ^ Jones, Lowell (1972). "The converse to the fixed point theorem of P. A. Smith" (PDF). Bulletin of the American Mathematical Society. 78 (2): 234. doi:10.1090/S0002-9904-1972-12934-3. JSTOR 1970734.
  4. ^ Farrell, F.T.; Jones, L.E. (1978). "Anosov diffeomorphisms constructed from π1 Diff (Sn)". Topology. 17 (3): 273–282. doi:10.1016/0040-9383(78)90031-9.
  5. ^ Farrell, F.T.; Jones, L.E. (Apr 1993). "Isomorphism Conjectures in Algebraic K-Theory". Journal of the American Mathematical Society. 2 (6): 249–297. doi:10.2307/2152801. JSTOR 2152801.
  6. ^ Davis, James (2012). "The Work of Tom Farrell and Lowell Jones in Topology and Geometry". Pure and Applied Mathematics Quarterly. 8 (1): 1–14. arXiv:1006.1489.
  7. ^ "Speakers at the ICM". Retrieved 21 December 2015.


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