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The title of the | '''Jeffrey Clark Lagarias''' (born November, 1949 in [[Pittsburgh, Pennsylvania|Pittsburgh]], [[Pennsylvania]], [[USA]]) is a [[mathematician]] and professor at the [[University of Michigan]]. | ||
== Education == | |||
While in high school in 1966, Lagarias studied [[astronomy]] at the [[Summer Science Program]]. | |||
He completed an S.B. and S.M. in Mathematics at the [[Massachusetts Institute of Technology]] in 1972.<ref name=cv>{{cite web|title=Jeffrey C. Lagarias|url=http://www.math.lsa.umich.edu/~lagarias/PROFESSIONAL/VITA/vita2013a.pdf|work=CV}}</ref> The title of his thesis was "Evaluation of certain character sums".<ref name=cv/> He was a [[Putnam Fellow]] at MIT in 1970.<ref name=cv/> He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974.<ref name=cv/><ref name=um>{{cite web|title=Jeffrey Lagarias, Professor|url=http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=lagarias|publisher=University of Michigan}}</ref> His advisor for both his masters and Ph.D was [[Harold Stark]].<ref name=cv/> | |||
== Career == | |||
In 1975 he joined [[AT&T Bell Laboratories]] and eventually became [[Distinguished Member of Technical Staff]]. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. In 2002, he moved to [[Michigan]] to work at the University and settle down with his family. | |||
While his recent work has been in [[theoretical computer science]], his original training was in analytic [[algebraic number theory]]. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Lagarias discovered an elementary problem that is equivalent to the [[Riemann hypothesis]], namely whether | |||
for all ''n'' > 0, we have | |||
:<math> \sigma(n) \le H_n + e^{H_n} \ln H_n \, </math> | |||
with equality only when ''n'' = 1. Here ''H''<sub>''n''</sub> is the ''n''th [[harmonic number]], the sum of the reciprocals of the first <math> n </math> positive integers, and ''σ''(''n'') is the [[divisor function]], the sum of the positive divisors of ''n''.<ref>http://front.math.ucdavis.edu/math.NT/0008177</ref> | |||
He disproved [[Keller's conjecture]] in dimensions at least 10. | |||
Lagarias has also done work on the [[Collatz conjecture]] and [[Li's criterion]]. | |||
==Awards and honors== | |||
In 1987 he received a [[Lester R. Ford]] award from the [[Mathematical Association of America]].<ref>http://oldweb.cecm.sfu.ca/CMS-95W/lagarias.html</ref> | |||
In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref> | |||
== External links == | |||
*{{MathGenealogy |id=36350}} | |||
*[http://www.math.lsa.umich.edu/~lagarias/ Jeffrey Clark Lagarias homepage], University of Michigan | |||
== References == | |||
{{reflist}} | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Lagarias, Jeffrey | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = American mathematician | |||
| DATE OF BIRTH = 1949 | |||
| PLACE OF BIRTH = | |||
| DATE OF DEATH = | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Lagarias, Jeffrey}} | |||
[[Category:1949 births]] | |||
[[Category:Living people]] | |||
[[Category:People from Pittsburgh, Pennsylvania]] | |||
[[Category:Massachusetts Institute of Technology alumni]] | |||
[[Category:Scientists at Bell Labs]] | |||
[[Category:20th-century mathematicians]] | |||
[[Category:21st-century mathematicians]] | |||
[[Category:Number theorists]] | |||
[[Category:American computer scientists]] | |||
[[Category:Theoretical computer scientists]] | |||
[[Category:University of Michigan faculty]] | |||
[[Category:Putnam Fellows]] | |||
[[Category:Summer Science Program]] | |||
[[Category:Fellows of the American Mathematical Society]] | |||
Revision as of 04:57, 23 January 2014
Jeffrey Clark Lagarias (born November, 1949 in Pittsburgh, Pennsylvania, USA) is a mathematician and professor at the University of Michigan.
Education
While in high school in 1966, Lagarias studied astronomy at the Summer Science Program.
He completed an S.B. and S.M. in Mathematics at the Massachusetts Institute of Technology in 1972.[1] The title of his thesis was "Evaluation of certain character sums".[1] He was a Putnam Fellow at MIT in 1970.[1] He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974.[1][2] His advisor for both his masters and Ph.D was Harold Stark.[1]
Career
In 1975 he joined AT&T Bell Laboratories and eventually became Distinguished Member of Technical Staff. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. In 2002, he moved to Michigan to work at the University and settle down with his family.
While his recent work has been in theoretical computer science, his original training was in analytic algebraic number theory. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Lagarias discovered an elementary problem that is equivalent to the Riemann hypothesis, namely whether for all n > 0, we have
with equality only when n = 1. Here Hn is the nth harmonic number, the sum of the reciprocals of the first positive integers, and σ(n) is the divisor function, the sum of the positive divisors of n.[3] He disproved Keller's conjecture in dimensions at least 10. Lagarias has also done work on the Collatz conjecture and Li's criterion.
Awards and honors
In 1987 he received a Lester R. Ford award from the Mathematical Association of America.[4]
In 2012 he became a fellow of the American Mathematical Society.[5]
External links
- 50 yr old Print Journalist Broadbent from Deep River, has hobbies and interests which includes r/c helicopters, property developers in singapore house for rent and scrabble. Suggests that you go to Tomb of Askia.
- Jeffrey Clark Lagarias homepage, University of Michigan
References
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- 1949 births
- Living people
- People from Pittsburgh, Pennsylvania
- Massachusetts Institute of Technology alumni
- Scientists at Bell Labs
- 20th-century mathematicians
- 21st-century mathematicians
- Number theorists
- American computer scientists
- Theoretical computer scientists
- University of Michigan faculty
- Putnam Fellows
- Summer Science Program
- Fellows of the American Mathematical Society