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Jonathan Lubin
Jonathan Darby Lubin (born August 10, 1936, in Staten Island, New York) is a professor emeritus of mathematics at Brown University. He received an A.B. from Columbia College in 1957 and a Ph.D. from Harvard University in 1963 under the direction of John Tate. He taught at Bowdoin College from 1962–1967 and at Brown University from 1967–2000. He and Tate introduced Lubin–Tate formal group laws and used them to construct explicit local class field theory In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credit .... References Home page of Jonathan LubinAnother home page of Jonathan Lubin* 20th-century American mathematicians 21st-century American mathematicians 1936 births Living people Harvard University alumni Brown University faculty Columbia College (New York) alum ... [...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] |
Brown University
Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providence Plantations. Brown is one of nine colonial colleges chartered before the American Revolution. Admissions at Brown is among the most selective in the United States. In 2022, the university reported a first year acceptance rate of 5%. It is a member of the Ivy League. Brown was the first college in the United States to codify in its charter that admission and instruction of students was to be equal regardless of their religious affiliation. The university is home to the oldest applied mathematics program in the United States, the oldest engineering program in the Ivy League, and the third-oldest medical program in New England. The university was one of the early doctoral-granting U.S. institutions in the late 19th century, adding masters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tate (mathematician)
John Torrence Tate Jr. (March 13, 1925 – October 16, 2019) was an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He was awarded the Abel Prize in 2010. Biography Tate was born in Minneapolis, Minnesota. His father, John Tate Sr., was a professor of physics at the University of Minnesota, and a longtime editor of ''Physical Review''. His mother, Lois Beatrice Fossler, was a high school English teacher. Tate Jr. received his bachelor's degree in mathematics in 1946 from Harvard University, and entered the doctoral program in physics at Princeton University. He later transferred to the mathematics department and received his PhD in mathematics in 1950 after completing a doctoral dissertation, titled "Fourier analysis in number fields and Hecke's zeta functions", under the supervision of Emil Artin. Tate taught at Harvard for 36 years before joining the Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staten Island, New York
Staten Island ( ) is a Boroughs of New York City, borough of New York City, coextensive with Richmond County, in the U.S. state of New York (state), New York. Located in the city's southwest portion, the borough is separated from New Jersey by the Arthur Kill and the Kill Van Kull and from the rest of New York by New York Bay. With a population of 495,747 in the 2020 United States Census, 2020 Census, Staten Island is the least populated borough but the third largest in land area at . A home to the Lenape indigenous people, the island was settled by Dutch colonists in the 17th century. It was one of the 12 original counties of New York state. Staten Island was City of Greater New York, consolidated with New York City in 1898. It was formally known as the Borough of Richmond until 1975, when its name was changed to Borough of Staten Island. Staten Island has sometimes been called "the forgotten borough" by inhabitants who feel neglected by the Government of New York City, city ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia College, Columbia University
Columbia College is the oldest undergraduate college of Columbia University, situated on the university's main campus in Morningside Heights in the borough of Manhattan in New York City. It was founded by the Church of England in 1754 as King's College, receiving a royal charter from King George II of Great Britain. It is the oldest institution of higher learning in the state of New York and the fifth oldest in the United States. Columbia College (along with Columbia Engineering) is distinctive for its comprehensive Core Curriculum and is among the most selective colleges in its admissions. History Columbia College was founded as King's College, by royal charter of King George II of Great Britain, in the Province of New York in 1754. Due in part to the influence of Church of England religious leaders, a site in New York City in the Trinity Church yard, Wall Street on the island of Manhattan was selected, however it would only remain at this site for less than a decade. ... [...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 Academic degree, 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 Thesis, 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 (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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bowdoin College
Bowdoin College ( ) is a private liberal arts college in Brunswick, Maine. When Bowdoin was chartered in 1794, Maine was still a part of the Commonwealth of Massachusetts. The college offers 34 majors and 36 minors, as well as several joint engineering programs with Columbia, Caltech, Dartmouth College, and the University of Maine. The college was a founding member of its athletic conference, the New England Small College Athletic Conference, and the Colby-Bates-Bowdoin Consortium, an athletic conference and inter-library exchange with Bates College and Colby College. Bowdoin has over 30 varsity teams, and the school mascot was selected as a polar bear in 1913 to honor Robert Peary, a Bowdoin alumnus who led the first successful expedition to the North Pole. Between the years 1821 and 1921, Bowdoin operated a medical school called the Medical School of Maine. The main Bowdoin campus is located near Casco Bay and the Androscoggin River. In addition to its Brunswick campus, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubin–Tate Formal Group Law
In mathematics, the Lubin–Tate formal group law is a formal group law introduced by to isolate the local field part of the classical theory of complex multiplication of elliptic functions. In particular it can be used to construct the totally ramified abelian extensions of a local field. It does this by considering the (formal) endomorphisms of the formal group, emulating the way in which elliptic curves with extra endomorphisms are used to give abelian extensions of global fields. Definition of formal groups Let Z''p'' be the ring of ''p''-adic integers. The Lubin–Tate formal group law is the unique (1-dimensional) formal group law ''F'' such that ''e''(''x'') = ''px'' + ''x''''p'' is an endomorphism of ''F'', in other words :e(F(x,y)) = F(e(x), e(y)).\ More generally, the choice for ''e'' may be any power series such that :''e''(''x'') = ''px'' + higher-degree terms and :''e''(''x'') = ''x''''p'' mod ''p''. All such group law ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing ''CF' ... [...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] |
