Lowell E. Jones: Difference between revisions
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==Mathematical contributions== |
==Mathematical contributions== |
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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. Thomas|author1-link=F. Thomas Farrell|last2=Jones|first2=Lowell E.|title=Anosov diffeomorphisms constructed from π1 Diff (Sn)|journal=[[Topology (journal)|Topology]]|date=1978|volume=17|issue=3|pages=273–282|doi=10.1016/0040-9383(78)90031-9|doi-access=free}}</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 |
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. Thomas|author1-link=F. Thomas Farrell|last2=Jones|first2=Lowell E.|title=Anosov diffeomorphisms constructed from π1 Diff (Sn)|journal=[[Topology (journal)|Topology]]|date=1978|volume=17|issue=3|pages=273–282|doi=10.1016/0040-9383(78)90031-9|doi-access=free}}</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. Thomas|author1-link=F. Thomas Farrell|last2=Jones|first2=Lowell 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 manifolds of dimension greater than four. |
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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|bibcode=2010arXiv1006.1489D|doi=10.4310/PAMQ.2012.v8.n1.a3|s2cid=55560396 }}</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|bibcode=2010arXiv1006.1489D|doi=10.4310/PAMQ.2012.v8.n1.a3|s2cid=55560396 }}</ref> |
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Revision as of 22:47, 20 October 2023
Lowell E. Jones | |
|---|---|
| Born | 1945 United States |
| Alma mater | Yale University |
| Known for | Farrell–Jones conjecture |
| Scientific career | |
| Fields | Geometry, Topology |
| Institutions | Stony Brook University |
| Doctoral advisor | Wu-Chung Hsiang |
Lowell Edwin 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 of Paul Althaus Smith.
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 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 manifolds of dimension 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
- ^ "Stony Brook Faculty page". Retrieved 20 December 2015.
- ^ Lowell E. Jones at the Mathematics Genealogy Project
- ^ Jones, Lowell (1972). "The converse to the fixed point theorem of P. A. Smith" (PDF). Bulletin of the American Mathematical Society. 78 (2): 234–236. doi:10.1090/S0002-9904-1972-12934-3. JSTOR 1970734.
- ^ Farrell, F. Thomas; Jones, Lowell E. (1978). "Anosov diffeomorphisms constructed from π1 Diff (Sn)". Topology. 17 (3): 273–282. doi:10.1016/0040-9383(78)90031-9.
- ^ Farrell, F. Thomas; Jones, Lowell 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.
- ^ 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. Bibcode:2010arXiv1006.1489D. doi:10.4310/PAMQ.2012.v8.n1.a3. S2CID 55560396.
- ^ "Speakers at the ICM". Retrieved 21 December 2015.
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