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Kevin Ford (mathematician)

Summary

Kevin B. Ford (born 22 December 1967) is an American mathematician working in analytic number theory.

Kevin B. Ford
Born (1967-12-22) 22 December 1967 (age 56)
NationalityAmerican
Alma materCalifornia State University, Chico
University of Illinois at Urbana-Champaign
Known for
Scientific career
FieldsMathematics
InstitutionsUniversity of Illinois at Urbana-Champaign
University of South Carolina
Doctoral advisorHeini Halberstam[1]

Education and career edit

He has been a professor in the department of mathematics of the University of Illinois at Urbana-Champaign since 2001. Prior to this appointment, he was a faculty member at the University of South Carolina.

Ford received a Bachelor of Science in Computer Science and Mathematics in 1990 from the California State University, Chico. He then attended the University of Illinois at Urbana-Champaign, where he completed his doctoral studies in 1994 under the supervision of Heini Halberstam.

Research edit

Ford's early work focused on the distribution of Euler's totient function. In 1998, he published a paper that studied in detail the range of this function and established that Carmichael's totient function conjecture is true for all integers up to  .[2] In 1999, he settled Sierpinski’s conjecture on Euler's totient function.[3]

In August 2014, Kevin Ford, in collaboration with Green, Konyagin and Tao,[4] resolved a longstanding conjecture of Erdős on large gaps between primes, also proven independently by James Maynard.[5] The five mathematicians were awarded for their work the largest Erdős prize ($10,000) ever offered. [6] In 2017, they improved their results in a joint paper. [7]

He is one of the namesakes of the Erdős–Tenenbaum–Ford constant,[8] named for his work using it in estimating the number of small integers that have divisors in a given interval.[9]

Recognition edit

In 2013, he became a fellow of the American Mathematical Society.[10]

References edit

  1. ^ Kevin Ford at the Mathematics Genealogy Project
  2. ^ Ford, Kevin (1998). "The distribution of totients". Ramanujan Journal. 2 (1–2): 67–151. arXiv:1104.3264. doi:10.1023/A:1009761909132. S2CID 6232638.
  3. ^ Ford, Kevin (1999). "The number of solutions of φ(x) = m". Annals of Mathematics. 150 (1). Princeton University and the Institute for Advanced Study: 283–311. doi:10.2307/121103. JSTOR 121103. Archived from the original on 2013-09-24. Retrieved 2019-04-19.
  4. ^ Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016). "Large gaps between consecutive primes". Annals of Mathematics. 183 (3): 935–974. arXiv:1408.4505. doi:10.4007/annals.2016.183.3.4. S2CID 16336889.
  5. ^ Maynard, James (2016). "Large gaps between primes". Annals of Mathematics. 183 (3). Princeton University and the Institute for Advanced Study: 915–933. arXiv:1408.5110. doi:10.4007/annals.2016.183.3.3. S2CID 119247836.
  6. ^ Klarreich, Erica (22 December 2014). "Mathematicians Make a Major Discovery About Prime Numbers". Wired. Retrieved 27 July 2015.
  7. ^ Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence (2018). "Long gaps between primes". Journal of the American Mathematical Society. 31: 65–105. arXiv:1412.5029. doi:10.1090/jams/876.
  8. ^ Luca, Florian; Pomerance, Carl (2014). "On the range of Carmichael's universal-exponent function" (PDF). Acta Arithmetica. 162 (3): 289–308. doi:10.4064/aa162-3-6. MR 3173026.
  9. ^ Koukoulopoulos, Dimitris (2010). "Divisors of shifted primes". International Mathematics Research Notices. 2010 (24): 4585–4627. arXiv:0905.0163. doi:10.1093/imrn/rnq045. MR 2739805. S2CID 7503281.
  10. ^ List of Fellows of the American Mathematical Society, retrieved 2017-11-03.