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Joseph Shalika
Joseph Andrew Shalika (June 25, 1941 – September 18, 2010) was a mathematician working on automorphic forms and representation theory, who introduced the multiplicity-one theorem. He was a member of the Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ... from 1965 to 1966. References * * External links *Professor Joseph Shalika (1941-2010) {{DEFAULTSORT:Shalika, Joseph 20th-century American mathematicians 21st-century American mathematicians 1941 births 2010 deaths Johns Hopkins University alumni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territories, nine Minor Outlying Islands, and 326 Indian reservations. The United States is also in free association with three Pacific Island sovereign states: the Federated States of Micronesia, the Marshall Islands, and the Republic of Palau. It is the world's third-largest country by both land and total area. It shares land borders with Canada to its north and with Mexico to its south and has maritime borders with the Bahamas, Cuba, Russia, and other nations. With a population of over 333 million, it is the most populous country in the Americas and the third most populous in the world. The national capital of the United States is Washington, D.C. and its most populous city and principal financial center is New York City. Paleo-Americ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johns Hopkins University
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consistently ranks among the most prestigious universities in the United States and the world. The university was named for its first benefactor, the American entrepreneur and Quaker philanthropist Johns Hopkins. Hopkins' $7 million bequest to establish the university was the largest Philanthropy, philanthropic gift in U.S. history up to that time. Daniel Coit Gilman, who was inaugurated as :Presidents of Johns Hopkins University, Johns Hopkins's first president on February 22, 1876, led the university to revolutionize higher education in the U.S. by integrating teaching and research. In 1900, Johns Hopkins became a founding member of the American Association of Universities. The university has led all Higher education in the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friederich Ignaz Mautner
Friederich Ignaz Mautner (14 May 1921–1996) was an Austrian-American mathematician, known for his research on the representation theory of groups, functional analysis, and differential geometry. He is known for Mautner's Lemma and Mautner's Phenomenon in the representation theory of Lie groups. Life and career Following the Anschluss in 1938, Mautner, a Jew, emigrated from Austria to the UK where he became one of the thousands or refugees who were interred by the British and shipped off to Hay Camp 7 in Australia. While there he was fortunate in that he got to study mathematics under Felix Behrend. When he got back to the UK, he garnered a BSc at Durham University and then went to Ireland in 1944 where he got an assistantship with Paul Ewald at Queens University Belfast (QUB). He then became a scholar at the Dublin Institute for Advanced Studies in 1944–1946. He then moved to the USA, where he was a visiting scholar at the Institute for Advanced Study (IAS) in Princeton ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freydoon Shahidi
Freydoon Shahidi (born June 19, 1947) is an Iranian American mathematician who is a Distinguished Professor of Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method.F. Shahidi, ''Eisenstein Series and Automorphic L-functions'', Colloquium Publications, Vol. 58, American Mathematical Society, Providence, Rhode Island, 2010. Education and career Shahidi graduated from the University of Tehran with a bachelor's degree in 1969. He received his Ph.D. in 1975 from Johns Hopkins University with dissertation ''On Gauss Sums Attached to the Pairs and the Exterior Powers of the Representations of the General Linear Groups over Finite and Local Fields'' with advisor Joseph Shalika. As a postdoc Shahidi was for the academic year 1975–1976 at the Institute for Advanced Study and for the academic year 1976–1977 a visiting assistant professor at Indiana University in Bloomington. At Purdue Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramin Takloo-Bighash
Ramin Takloo-Bighash (born 1974) is a mathematician who works in the field of automorphic forms and Diophantine geometry and is a professor at the University of Illinois at Chicago. Mathematical career Takloo-Bighash graduated from the Sharif University of Technology, where he enrolled after winning a Silver medal at the 1992 International Mathematical Olympiad. In 2001, Takloo-Bighash graduated under Joseph Shalika from Johns Hopkins University. He spent 2001-2007 at Princeton University, first as an instructor and then as an assistant professor. He is a professor at the University of Illinois at Chicago. Research Takloo-Bighash computed the local factors of spinor L-function attached to generic automorphic forms on the symplectic group GSp(4). He has joint works with Joseph Shalika and Yuri Tschinkel on the distribution of rational point In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphic Form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms. More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group ''G''(A''F''), for an algebraic group ''G'' and an algebraic number field ''F'', is a complex-valued function on ''G''(A''F'') that is left ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicity-one Theorem
In the mathematical theory of automorphic representations, a multiplicity-one theorem is a result about the representation theory of an adelic reductive algebraic group. The multiplicity in question is the number of times a given abstract group representation is realised in a certain space, of square-integrable functions, given in a concrete way. A multiplicity one theorem may also refer to a result about the restriction of a representation of a group ''G'' to a subgroup ''H''. In that context, the pair (''G'', ''H'') is called a strong Gelfand pair. Definition Let ''G'' be a reductive algebraic group over a number field ''K'' and let A denote the adeles of ''K''. Let ''Z'' denote the centre of ''G'' and let be a continuous unitary character from ''Z''(''K'')\Z(A)× to C×. Let ''L''20(''G''(''K'')/''G''(A), ) denote the space of cusp forms with central character ω on ''G''(A). This space decomposes into a direct sum of Hilbert spaces :L^2_0(G(K) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contracted or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
