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Sir Andrew John Wiles is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal and for which he was appointed a Knight Commander of the Order of the British Empire in 2000. In 2018, Wiles was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow.
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
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.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory.
In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo almost all prime numbers p. Mikio Sato and John Tate independently posed the conjecture around 1960.
Richard Lawrence Taylor is a British mathematician working in the field of number theory. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University.
Hilbert's twelfth problem is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field. It is one of the 23 mathematical Hilbert problems and asks for analogues of the roots of unity that generate a whole family of further number fields, analogously to the cyclotomic fields and their subfields. Leopold Kronecker described the complex multiplication issue as his liebster Jugendtraum, or "dearest dream of his youth", so the problem is also known as Kronecker's Jugendtraum.
Brian Conrad is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University.
Kevin Mark Buzzard is a British mathematician and currently a professor of pure mathematics at Imperial College London. He specialises in arithmetic geometry and the Langlands program.
Alexander A. Beilinson is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017, he was elected to the National Academy of Sciences. In 2018, he received the Wolf Prize in Mathematics and in 2020 the Shaw Prize in Mathematics.
Michael Howard Harris is an American mathematician known for his work in number theory. He is a professor of mathematics at Columbia University and professor emeritus of mathematics at Université Paris Cité.
In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galois group to a subgroup.
Ana Caraiani is a Romanian-American mathematician, who is a Royal Society University Research Fellow and Hausdorff Chair at the University of Bonn. Her research interests include algebraic number theory and the Langlands program.
Sarah Livia Zerbes is a German algebraic number theorist at ETH Zurich. Her research interests include L-functions, modular forms, p-adic Hodge theory, and Iwasawa theory, and her work has led to new insights towards the Birch and Swinnerton-Dyer conjecture, which predicts the number of rational points on an elliptic curve by the behavior of an associated L-function.
Kari Kaleva Vilonen is a Finnish mathematician, specializing in geometric representation theory. He is currently a professor at the University of Melbourne.
Jack A. Thorne is a British mathematician working in number theory and arithmetic aspects of the Langlands Program. He specialises in algebraic number theory.
Christopher McLean Skinner is an American mathematician and professor at Princeton University. He works in algebraic number theory and arithmetic aspects of the Langlands program.
Andrew Victor Sutherland is an American mathematician and Principal Research Scientist at the Massachusetts Institute of Technology. His research focuses on computational aspects of number theory and arithmetic geometry. He is known for his contributions to several projects involving large scale computations, including the Polymath project on bounded gaps between primes, the L-functions and Modular Forms Database, the sums of three cubes project, and the computation and classification of Sato-Tate distributions.
Sug Woo Shin is a professor of mathematics at the University of California, Berkeley working in number theory, automorphic forms, and the Langlands program.
References
- ↑ "Prizes 2012" (PDF). London Mathematical Society.
- ↑ "Philip Leverhulme Prize Winners 2012" (PDF). The Leverhulme Trust.
- ↑ "2014 Class of the Fellows of the AMS" (PDF). American Mathematical Society.
- ↑ "Curriculum vitae" (PDF). Imperial College. Retrieved 7 April 2024.
- ↑ Gee, Toby; Kisin, Mark (December 2014). "The Breuil–Mézard Conjecture For Potentially Barsotti–Tate Representations". Forum of Mathematics, Pi. 2. arXiv: 1208.3179 . doi:10.1017/fmp.2014.1. ISSN 2050-5086. S2CID 16351884.
- ↑ Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David (2011). "The Sato–Tate conjecture for Hilbert modular forms". Journal of the American Mathematical Society. 24 (2): 411–469. arXiv: 0912.1054 . doi:10.1090/S0894-0347-2010-00689-3. ISSN 0894-0347. S2CID 12534084.
- ↑ "Prizewinners 2012". Bulletin of the London Mathematical Society. 45 (2): 421–428. 1 April 2013. doi:10.1112/blms/bdt015. ISSN 0024-6093. S2CID 247674468.
