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Nicholas Katz
Nicholas Michael Katz (born December 7, 1943) is an American mathematician, working in arithmetic geometry, particularly on ''p''-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at Princeton University and an editor of the journal ''Annals of Mathematics''. Life and work Katz graduated from Johns Hopkins University (BA 1964) and from Princeton University, where in 1965 he received his master's degree and in 1966 he received his doctorate under supervision of Bernard Dwork with thesis ''On the Differential Equations Satisfied by Period Matrices''. After that, at Princeton, he was an instructor, an assistant professor in 1968, associate professor in 1971 and professor in 1974. From 2002 to 2005 he was the chairman of faculty there. He was also a visiting scholar at the University of Minnesota, the University of Kyoto, Paris VI, Orsay Faculty of Sciences, the Institute for Advanced Study and the IHES. While in Franc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baltimore
Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was designated an independent city by the Constitution of Maryland in 1851, and today is the most populous independent city in the United States. As of 2021, the population of the Baltimore metropolitan area was estimated to be 2,838,327, making it the 20th largest metropolitan area in the country. Baltimore is located about north northeast of Washington, D.C., making it a principal city in the Washington–Baltimore combined statistical area (CSA), the third-largest CSA in the nation, with a 2021 estimated population of 9,946,526. Prior to European colonization, the Baltimore region was used as hunting grounds by the Susquehannock Native Americans, who were primarily settled further northwest than where the city was later built. Colonist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scheme Theory
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations ''x'' = 0 and ''x''2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise "Éléments de géométrie algébrique"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra. Scheme theory also unifies algebraic geometry with much of number theory, which eventually led to Wiles's proof of Fermat's Last Theorem. Formally, a scheme is a topological space together with commu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institut Des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, just south of Paris. It is an independent research institute in a partnership with the University of Paris-Saclay. History The IHÉS was founded in 1958 by businessman and mathematical physicist Léon Motchane with the help of Robert Oppenheimer and Jean Dieudonné as a research centre in France, modeled on the renowned Institute for Advanced Study in Princeton, United States. The strong personality of Alexander Grothendieck and the broad sweep of his revolutionizing theories were a dominating feature of the first ten years at the IHÉS. René Thom received an invitation from IHÉS in 1963 and after his appointment remained there until his death in 2002. Dennis Sullivan is remembered as one who had a special talent for encouraging fruitf ... [...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] |
Orsay Faculty Of Sciences
The Paris-Saclay Faculty of Sciences or Orsay Faculty of Sciences, in French : ''Faculté des sciences d'Orsay'', is the mathematics and physics school within Paris-Saclay University, founded in 1956. It offers undergraduate and graduate degrees in mathematics, physics and chemistry (though its undergraduates are officially enrolled in Paris-Saclay Undergraduate School). Previously the Paris-Sud Faculty of Sciences, the School assumed its current structure in 2019. Christine Paulin-Mohring has been the School's dean since 2016. Recent investments as part of the Paris-Saclay cluster have enlarged the School's faculty and upgraded its facilities. In July 2020, Paris-Saclay was ranked first worldwide for Mathematics by '' Academic Ranking of World Universities (ARWU)'' and 9th worldwide for Physics (1st in Europe). The Faculty has produced numerous research discoveries and many distinguished alumni and professors. History Established in 1956, the Paris-Saclay Faculty of Scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pierre And Marie Curie
Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, France. UPMC merged with Paris-Sorbonne University into a new combined Sorbonne University. It was ranked as the best university in France in medicine and health sciences by ''Times Higher Education'' in 2018. History Paris VI was one of the inheritors of the faculty of Sciences of the University of Paris, which was divided into several universities in 1970 after the student protests of May 1968. In 1971, the five faculties of the former University of Paris (Paris VI as the Faculty of Sciences) were split and then re-formed into thirteen universities by the Faure Law. The campus of Paris VI was built in the 1950s and 1960s, on a site previously occupied by wine storehouses. The Dean, Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Kyoto
, mottoeng = Freedom of academic culture , established = , type = Public (National) , endowment = ¥ 316 billion (2.4 billion USD) , faculty = 3,480 (Teaching Staff) , administrative_staff = 3,978 (Total Staff) , students = 22,615 , president = Nagahiro Minato , city = Kyoto , state = Kyoto , country = Japan , coor = , undergrad = 13,038 , postgrad = 9,308 , campus = Urban,, , colors = Dark blue , nickname = Kyodai , mascot = None , free_label = Athletics , free = 48 varsity teams , affiliations = Kansai Big Six, ASAIHL , logo = , website www.kyoto-u.ac.jp , or , is a public research university located in Kyoto, Japan. Founded in 1897, it is one of the former Imperial Universities and the second oldest university in Japan. KyotoU is consistently ranked amongst the top two in Japan, the top ten in Asia, and the world's top fifty institutions of higher education. Founded upon the principles of its motto, “fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Minnesota
The University of Minnesota, formally the University of Minnesota, Twin Cities, (UMN Twin Cities, the U of M, or Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint Paul, Minnesota, United States. The Twin Cities campus comprises locations in Minneapolis and Falcon Heights, Minnesota, Falcon Heights, a suburb of St. Paul, approximately apart. The Twin Cities campus is the oldest and largest in the University of Minnesota system and has the List of United States university campuses by enrollment, ninth-largest main campus student body in the United States, with 52,376 students at the start of the 2021–22 academic year. It is the Flagship#Colleges and universities in the United States, flagship institution of the University of Minnesota System, and is organized into 19 colleges, schools, and other major academic units. The Minnesota Territorial Legislature drafted a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...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 arithmetic function, 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 Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Problem
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
