Cameron Leigh Stewart | |
|---|---|
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| Nationality | Canadian |
| Alma mater | University of Cambridge McGill University University of British Columbia |
| Awards | J. T. Knight Prize (1974) Fellow of the Royal Society of Canada (1989) Fields Institute Fellow (2008) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Waterloo |
| Doctoral advisor | Alan Baker |
Cameron Leigh Stewart FRSC is a Canadian mathematician. He is a professor of pure mathematics at the University of Waterloo.
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 is at most , where is a pre-determined positive real number and is the number of distinct primes dividing a large divisor of . 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 of satisfies .
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. [1]
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). [2] Since 2005 he has been appointed University Professor at the University of Waterloo. [3] He was selected to give the annual Isidore and Hilda Dressler Lecture at Kansas State University in 2015.
He was elected as a fellow of the Canadian Mathematical Society in 2019. [4]
The abc conjecture is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers and that are relatively prime and satisfy . The conjecture essentially states that the product of the distinct prime factors of is usually not much smaller than . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician Dorian Goldfeld described the abc conjecture as "The most important unsolved problem in Diophantine analysis".
The modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves, which was enough to imply Fermat's Last Theorem. Later, a series of papers by Wiles's former students Brian Conrad, Fred Diamond and Richard Taylor, culminating in a joint paper with Christophe Breuil, extended Wiles's techniques to prove the full modularity theorem in 2001.
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.
John Lewis Selfridge, was an American mathematician who contributed to the fields of analytic number theory, computational number theory, and combinatorics.
Jean Louis, baron Bourgain was a Belgian mathematician. He was awarded the Fields Medal in 1994 in recognition of his work on several core topics of mathematical analysis such as the geometry of Banach spaces, harmonic analysis, ergodic theory and nonlinear partial differential equations from mathematical physics.
In mathematics, a Thue equation is a Diophantine equation of the form
The Ramanujan tau function, studied by Ramanujan, is the function defined by the following identity:
The Beal conjecture is the following conjecture in number theory:
In number theory, Grimm's conjecture states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. It was first published in American Mathematical Monthly, 76(1969) 1126-1128.
In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation
In algebraic geometry, flips and flops are codimension-2 surgery operations arising in the minimal model program, given by blowing up along a relative canonical ring. In dimension 3 flips are used to construct minimal models, and any two birationally equivalent minimal models are connected by a sequence of flops. It is conjectured that the same is true in higher dimensions.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.
The Mason–Stothers theorem, or simply Mason's theorem, is a mathematical theorem about polynomials, analogous to the abc conjecture for integers. It is named after Walter Wilson Stothers, who published it in 1981, and R. C. Mason, who rediscovered it shortly thereafter.
In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper Witten, and generalized in Witten (1993). Witten's original conjecture was proved by Maxim Kontsevich in the paper Kontsevich (1992).
In mathematics, a superelliptic curve is an algebraic curve defined by an equation of the form
In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after Shoshichi Kobayashi and Nigel Hitchin, who independently conjectured in the 1980s that the moduli spaces of stable vector bundles and Einstein–Hermitian vector bundles over a complex manifold were essentially the same.
In mathematics, the Simon problems are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential.
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