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Richard Taylor (mathematician)
Richard Lawrence Taylor (born 19 May 1962) 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. Taylor received the 2015 Breakthrough Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato–Tate conjecture." He also received the 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands. He also served on the Mathematical Sciences jury for the Infosys Prize from 2012 to 2014. Career He received his B.A. from Clare College, Cambridge.SAVILIAN PROFESSORSHIP OF GEOMETRY in NOTICES, University Gazette 23.3.95 No. 435 During his time at University of Cambridge, Cambridge, he was president of The Archimedeans in 1981 and 1982, following the resignation of his predecessor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clare College, Cambridge
Clare College is a constituent college of the University of Cambridge in Cambridge, England. The college was founded in 1326 as University Hall, making it the second-oldest surviving college of the University after Peterhouse. It was refounded in 1338 as ''Clare Hall'' by an endowment from Elizabeth de Clare, and took on its current name in 1856. Clare is famous for its chapel choir and for its gardens on " The Backs" (the back of the colleges that overlook the River Cam). Clare is consistently one of the most popular Cambridge colleges amongst prospective applicants. History The college was founded in 1326 by the university's Chancellor, Richard Badew, and was originally named ''University Hall''. Providing maintenance for only two fellows, it soon hit financial hardship. In 1338, the college was refounded as ''Clare Hall'' by an endowment from Elizabeth de Clare, a granddaughter of Edward I, which provided for twenty fellows and ten students. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Form
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory. A modular function is a function that is invariant with respect to the modular group, but without the condition that be holomorphic in the upper half-plane (among other requirements). Instead, modular functions are meromorphic (that is, they are holomorphic on the complement of a set of isolated points, which are poles of the function). Modular form theory is a special case of the more general theory of automorphic forms which are functions defined on Lie groups which transform nicely w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Archimedeans
The Archimedeans are the mathematical society of the University of Cambridge, founded in 1935. It currently has over 2000 active members, many of them alumni, making it one of the largest student societies in Cambridge. The society hosts regular talks at the Centre for Mathematical Sciences, including in the past by many well-known speakers in the field of mathematics. It publishes two magazines, ''Eureka'' and ''QARCH''. One of several aims of the society, as laid down in its constitution, is to encourage co-operation between the existing mathematical societies of individual Cambridge colleges, which at present are just the Adam's society of St John's College and the Trinity Mathematical Society, but in the past have included many more. The society is mentioned in G. H. Hardy's essay A Mathematician's Apology. Past presidents of The Archimedeans include Michael Atiyah and Richard Taylor. Activity The main focus of the society's activities are the regular talks, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cambridge
The University of Cambridge is a public collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III in 1231, Cambridge is the world's third oldest surviving university and one of its most prestigious, currently ranked second-best in the world and the best in Europe by '' QS World University Rankings''. Among the university's most notable alumni are 11 Fields Medalists, seven Turing Award winners, 47 heads of state, 14 British prime ministers, 194 Olympic medal-winning athletes,All Known Cambridge Olympians . ''Hawks Club''. Retrieved 17 May 2019. and some of world history's most transformational and iconic figures across disciplines, including [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bachelor Of Arts
Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four years, depending on the country and institution. * Degree attainment typically takes four years in Afghanistan, Armenia, Azerbaijan, Bangladesh, Brazil, Brunei, China, Egypt, Ghana, Greece, Georgia, Hong Kong, Indonesia, Iran, Iraq, Ireland, Japan, Kazakhstan, Kenya, Kuwait, Latvia, Lebanon, Lithuania, Mexico, Malaysia, Mongolia, Myanmar, Nepal, Netherlands, Nigeria, Pakistan, the Philippines, Qatar, Russia, Saudi Arabia, Scotland, Serbia, South Korea, Spain, Sri Lanka, Taiwan, Thailand, Turkey, Ukraine, the United States and Zambia. * Degree attainment typically takes three years in Albania, Australia, Bosnia and Herzegovina, the Caribbean, Iceland, India, Israel, Italy, New Zealand, Norway, South Africa, Switzerland, the Canadian province o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infosys Prize
The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to recognize research. The prize for each category includes a gold medallion, a citation certificate, and prize money of US$100,000 (or its equivalent in Indian Rupees). The prize purse is tax free in the hands of winners in India. The winners are selected by the jury of their respective categories, headed by the jury chairs. In 2008, the prize was jointly awarded by the Infosys Science Foundation and National Institute of Advanced Studies for mathematics. The following year, three additional categories were added: Life Sciences, Mathematical Sciences, Physical Sciences and Social Sciences. In 2010, Engineering and Computer Science was added as a category. In 2012, a sixth category, Humanities, was added. Laureates in Engineering and Compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Langlands
Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received the 2018 Abel Prize. He was an emeritus professor and occupied Albert Einstein's office at the Institute for Advanced Study in Princeton, until 2020 when he retired. Career Langlands was born in New Westminster, British Columbia, Canada, in 1936 to Robert Langlands and Kathleen J Phelan. He has two younger sisters (Mary b 1938; Sally b 1941). In 1945, his family moved to White Rock, near the US border, where his parents had a building supply and construction business. He graduated from Semiahmoo Secondary School and started enrolling at the University of British Columbia at the age of 16, receiving his undergraduate degree in Mathematics in 1957; he continued at UBC to receive an M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langlands Program
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , 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 Langlands program consists of some very complicated theoretical abstractions, which can be difficult even for specialist mathematicians to grasp. To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sato–Tate Conjecture
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. If ''Np'' denotes the number of points on the elliptic curve ''Ep'' defined over the finite field with ''p'' elements, the conjecture gives an answer to the distribution of the second-order term for ''Np''. By Hasse's theorem on elliptic curves, :N_p/p = 1 + \mathrm(1/\!\sqrt)\ as p\to\infty, and the point of the conjecture is to predict how the O-term varies. The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011. Several generalizations to other algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Linear Group
In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns (and also the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position. To be more precise, it is necessary to specify what kind of objects may appear in the entries of the matrix. For example, the general linear group over R (the set of real numbers) is the group of invertible matrices of real numbers, and is denoted by GL''n''(R) or . More generally, the general linear group of degree ''n'' over an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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