Cameron Leigh Stewart

He has made numerous contributions to number theory, in particular to work on the abc conjecture. In 1976 he obtained, with Alan Baker, an effective improvement to Liouville's Theorem. In 1991 he proved that the number of solutions to a Thue equation $f(x,y)\; =\; h$ is at most $2800(1\; +\; 1/4\backslash epsilon\; \backslash deg\; f)(\backslash deg\; f)^\{1\; +\; \backslash omega(g)\}$, where $\backslash epsilon$ is a pre-determined positive real number and $\backslash omega(g)$ is the number of distinct primes dividing a large divisor $g$ of $h$. This improves on an earlier result of Enrico Bombieri and Wolfgang M. Schmidt and is close to the best possible result. In 1995 he obtained, along with Jaap Top, the existence of infinitely many quadratic, cubic, and sextic twists of elliptic curves of large rank. In 1991 and 2001 respectively, he obtained, along with Kunrui Yu, the best unconditional estimates for the abc conjecture. In 2013, he solved an old problem of Erdős (so his Erdős number is 1) involving Lucas and Lehmer numbers. In particular, he proved that the largest prime divisor $P(n)$ of $2^n\; -\; 1$ satisfies $\backslash lim\_\{n\; \backslash rightarrow\; \backslash infty\}\; P(n)/n\; =\; \backslash infty$.

Stewart completed a B.Sc. at the University of British Columbia in 1971 and a M.Sc in 1972 from McGill University. He earned his doctorate from the University of Cambridge in 1976, under the supervision of Alan Baker.[http://math.uwaterloo.ca/pure-mathematics/people-profiles/cameron-l-stewart/curriculum-vitae Curriculum Vitae at University of Waterloo]

In 1974, while at Cambridge, he was awarded the J.T. Knight Prize.

He was elected Fellow of the Royal Society of Canada in 1989. He was appointed Fellow of the Fields Institute in 2008. Since 2003 he has held a Canada Research Chair (tier 1).[http://www.chairs-chaires.gc.ca/chairholders-titulaires/profile-eng.aspx?profileId=2632 Cameron L. Stewart's Canada Research Chair Profile] Since 2005 he has been appointed University Professor at the University of Waterloo.University Professors of the University of Waterloo http://provost.uwaterloo.ca/universityprofessors.html He was selected to give the annual [https://web.archive.org/web/20130620202326/http://www.math.ksu.edu/group/numbertheory/dressler.html Isidore and Hilda Dressler Lecture] at Kansas State University in 2015.

He was elected as a fellow of the Canadian Mathematical Society in 2019.{{citation|url=https://cms.math.ca/MediaReleases/2019/Fellows|title=Canadian Mathematical Society's Second Inaugural Class of Fellows Announced|publisher=Canadian Mathematical Society|access-date=2020-01-06}}

• {{Cite journal |last1=Stewart |first1=C. L. |last2=Tijdeman |first2=R. |year=1986 |title=On the Oesterlé-Masser conjecture |journal=Monatshefte für Mathematik |volume=102 |issue=3 |pages=251–257 |doi=10.1007/BF01294603 |s2cid=123621917 }}
• {{Cite journal |last1=Erdős |first1=P. |author-link=Paul Erdős |last2=Stewart |first2=C. L. |last3=Tijdeman |first3=R. |year=1988 |title=Some diophantine equations with many solutions |journal=Compositio Mathematica |volume=66 |issue=1 |pages=37–56 }}
• {{Cite journal |last=Stewart |first=C.L. |year=1991 |title=On the number of solutions of polynomial congruences and Thue equations |journal=J. Amer. Math. Soc. |volume=4 |issue=4 |pages=793–835 |mr=1119199 |doi=10.1090/s0894-0347-1991-1119199-x|doi-access=free }}
• {{Cite journal |last=Stewart |first=C. L. |author2=Kunrui Yu |year=1991 |title=On the abc conjecture |journal=Mathematische Annalen |volume=291 |issue=1 |pages=225–230 |doi=10.1007/BF01445201 |s2cid=123894587 }}
• {{Cite journal |last1=Stewart |first1=C. L. |last2=Top |first2=J. |title=On ranks of twists of elliptic curves and power-free values of binary forms |journal=J. Amer. Math. Soc. |year=1995 |volume=8 |issue=4 |pages=943–973 |mr=1290234 |doi=10.1090/s0894-0347-1995-1290234-5|doi-access=free }}
• {{Cite journal |last=Stewart |first=C. L. |author2=Kunrui Yu |s2cid=14862375 |year=2001 |title=On the abc conjecture, II |journal=Duke Math. J. |volume=108 |issue=1 |pages=169–181 | mr = 1831823 |doi=10.1215/s0012-7094-01-10815-6}}
• {{Cite journal |last=Stewart |first=C. L. |title=On divisors of Lucas and Lehmer numbers |journal=Acta Math. |year=2013 |volume=211 |issue=2 |pages=291–314 |mr=3143892 |doi=10.1007/s11511-013-0105-y|arxiv=1008.1274 |s2cid=119666101 }}

{{Reflist}}

• [http://math.uwaterloo.ca/pure-mathematics/people-profiles/cameron-l-stewart Website at University of Waterloo]
• {{MathGenealogy |id=38813 }}

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Category:Abc conjecture