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Charles Fefferman
Charles Louis Fefferman (born April 18, 1949) is an American mathematician at Princeton University, where he is currently the Herbert E. Jones, Jr. '43 University Professor of Mathematics. He was awarded the Fields Medal in 1978 for his contributions to mathematical analysis. Early life and education Fefferman was born to a Jewish family, in Washington, DC. Fefferman was a child prodigy. Fefferman entered the University of Maryland at age 14, and had written his first scientific paper by the age of 15. He graduated with degrees in math and physics at 17, and earned his PhD in mathematics three years later from Princeton University, under Elias Stein. His doctoral dissertation was titled "Inequalities for strongly singular convolution operators". Fefferman achieved a full professorship at the University of Chicago at the age of 22, making him the youngest full professor ever appointed in the United States. Career At the age of 25, he returned to Princeton as a full professor, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Child Prodigy
A child prodigy is defined in psychology research literature as a person under the age of ten who produces meaningful output in some domain at the level of an adult expert. The term is also applied more broadly to young people who are extraordinarily talented in some field. The term ''Wunderkind'' (from German ''Wunderkind''; literally "wonder child") is sometimes used as a synonym for child prodigy, particularly in media accounts. ''Wunderkind'' also is used to recognize those who achieve success and acclaim early in their adult careers. Examples Memory capacity of prodigies PET scans performed on several mathematics prodigies have suggested that they think in terms of long-term working memory (LTWM). This memory, specific to a field of expertise, is capable of holding relevant information for extended periods, usually hours. For example, experienced waiters have been found to hold the orders of up to twenty customers in their heads while they serve them, but perform only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergman Kernel
In the mathematical study of several complex variables, the Bergman kernel, named after Stefan Bergman, is the reproducing kernel for the Hilbert space (RKHS) of all square integrable holomorphic functions on a domain ''D'' in C''n''. In detail, let L2(''D'') be the Hilbert space of square integrable functions on ''D'', and let ''L''2,''h''(''D'') denote the subspace consisting of holomorphic functions in L2(''D''): that is, :L^(D) = L^2(D)\cap H(D) where ''H''(''D'') is the space of holomorphic functions in ''D''. Then ''L''2,''h''(''D'') is a Hilbert space: it is a closed linear subspace of ''L''2(''D''), and therefore complete in its own right. This follows from the fundamental estimate, that for a holomorphic square-integrable function ''ƒ'' in ''D'' for every compact subset ''K'' of ''D''. Thus convergence of a sequence of holomorphic functions in ''L''2(''D'') implies also compact convergence, and so the limit function is also holomorphic. Another consequence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotics
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lennart Carleson
Lennart Axel Edvard Carleson (born 18 March 1928) is a Swedish mathematician, known as a leader in the field of harmonic analysis. One of his most noted accomplishments is his proof of Lusin's conjecture. He was awarded the Abel Prize in 2006 for "his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems." Life He was a student of Arne Beurling and received his Ph.D. from Uppsala University in 1950. He did his post-doctoral work at Harvard University where he met and discussed Fourier series and their convergence with Antoni Zygmund and Raphaël Salem who were there in 1950 and 1951. He is a professor emeritus at Uppsala University, the Royal Institute of Technology in Stockholm, and the University of California, Los Angeles, and has served as director of the Mittag-Leffler Institute in Djursholm outside Stockholm 1968–1984. Between 1978 and 1982 he served as president of the International Mathematical Union. Carleson married Butte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helsinki
Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of Uusimaa in southern Finland, and has a population of . The Helsinki urban area, city's urban area has a population of , making it by far the List of urban areas in Finland by population, most populous urban area in Finland as well as the country's most important center for politics, education, finance, culture, and research; while Tampere in the Pirkanmaa region, located to the north from Helsinki, is the second largest urban area in Finland. Helsinki is located north of Tallinn, Estonia, east of Stockholm, Sweden, and west of Saint Petersburg, Russia. It has History of Helsinki, close historical ties with these three cities. Together with the cities of Espoo, Vantaa, and Kauniainen (and surrounding commuter towns, including the eastern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Spaces
In complex analysis, the Hardy spaces (or Hardy classes) ''Hp'' are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the ''Lp'' spaces of functional analysis. For 1 ≤ ''p'' < ∞ these real Hardy spaces ''Hp'' are certain subsets of ''Lp'', while for ''p'' < 1 the ''Lp'' spaces have some undesirable properties, and the Hardy spaces are much better behaved. There are also higher-dimensional generalizations, consisting of certain holomorphic functions on |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and community outreach. Considered the first learned society in the United States, it has about 1,000 elected members, and by April 2020 had had only 5,710 members since its creation. Through research grants, published journals, the American Philosophical Society Museum, an extensive library, and regular meetings, the society supports a variety of disciplines in the humanities and the sciences. Philosophical Hall, now a museum, is just east of Independence Hall in Independence National Historical Park; it was designated a National Historic Landmark in 1965. History The Philosophical Society, as it was originally called, was founded in 1743 by Benjamin Franklin, James Alexander (lawyer), James Alexander, Francis Hopkinson, John Bartram, Philip Syn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Academy Of Arts And Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other Founding Fathers of the United States. It is headquartered in Cambridge, Massachusetts. Membership in the academy is achieved through a thorough petition, review, and election process. The academy's quarterly journal, ''Dædalus'', is published by MIT Press on behalf of the academy. The academy also conducts multidisciplinary public policy research. History The Academy was established by the Massachusetts legislature on May 4, 1780, charted in order "to cultivate every art and science which may tend to advance the interest, honor, dignity, and happiness of a free, independent, and virtuous people." The sixty-two incorporating fellows represented varying interests and high standing in the political, professional, and commercial secto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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