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Ralph Greenberg
Ralph Greenberg (born 1944) is an American mathematician who has made contributions to number theory, in particular Iwasawa theory. He was born in Chester, Pennsylvania and studied at the University of Pennsylvania, earning a B.A. in 1966, after which he attended Princeton University, earning his doctorate in 1971 under the supervision of Kenkichi Iwasawa. Greenberg's results include a proof (joint with Glenn Stevens (mathematician), Glenn Stevens) of the Mazur–Tate–Teitelbaum conjecture as well as a formula for the derivative of a p-adic L-function, ''p''-adic Dirichlet ''L''-function at s=0 (joint with Bruce Ferrero). Greenberg is also well known for Greenberg's conjectures, his many conjectures. In his PhD thesis, he conjectured that the Iwasawa μ- and λ-invariants of the cyclotomic \Z_p-extension of a totally real field are zero, a conjecture that remains open as of September 2012. In the 1980s, he introduced the notion of a Selmer group for a p-adic Galois representati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chester, Pennsylvania
Chester is a city in Delaware County, Pennsylvania, United States. Located within the Philadelphia Metropolitan Area, it is the only city in Delaware County and had a population of 32,605 as of the 2020 census. Incorporated in 1682, Chester is the oldest city in Pennsylvania and is located on the western bank of the Delaware River between the cities of Philadelphia and Wilmington, Delaware. It was the location of William Penn's first arrival in the Province of Pennsylvania and the county seat for Chester County from 1682 to 1788 and Delaware County from 1789 to 1851. Chester evolved over the centuries from a small town with wooden shipbuilding and textile factories into an industrial powerhouse producing steel ships for two World Wars and a myriad of consumer goods. Since the mid-twentieth century, it has lost its manufacturing base and over half of its residents and devolved into a post-industrial city struggling with pollution, poverty, and crime. History Early history Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Totally Real Field
In number theory, a number field ''F'' is called totally real if for each embedding of ''F'' into the complex numbers the image lies inside the real numbers. Equivalent conditions are that ''F'' is generated over Q by one root of an integer polynomial ''P'', all of the roots of ''P'' being real; or that the tensor product algebra of ''F'' with the real field, over Q, is isomorphic to a tensor power of R. For example, quadratic fields ''F'' of degree 2 over Q are either real (and then totally real), or complex, depending on whether the square root of a positive or negative number is adjoined to Q. In the case of cubic fields, a cubic integer polynomial ''P'' irreducible over Q will have at least one real root. If it has one real and two complex roots the corresponding cubic extension of Q defined by adjoining the real root will ''not'' be totally real, although it is a field of real numbers. The totally real number fields play a significant special role in algebraic number theory. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cydonia (Mars)
Cydonia (, ) is a region on the planet Mars that has attracted both scientific and popular interest. The name originally referred to the albedo feature (distinctively coloured area) that was visible from earthbound telescopes. The area borders the plains of Acidalia Planitia and the highlands of Arabia Terra. The region includes the named features Cydonia Mensae, an area of flat-topped mesa-like features; Cydonia Colles, a region of small hills or Mountain, knobs; and Cydonia Labyrinthus, a complex of intersecting valleys. As with other albedo features on Mars, the name Cydonia was Classical albedo features on Mars#B-E, drawn from classical antiquity, in this case from ''Kydonia'' ( grc, Κυδωνία; lat, Cydonia), a historic ''polis'' (city state) on the island of Crete. Cydonia contains the "Face on Mars", located about halfway between the craters Arandas (crater), Arandas and Bamberg (crater), Bamberg. Location Cydonia lies in the planet's northern hemisphere in a transit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard C
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include "Richie", "Dick", "Dickon", " Dickie", "Rich", "Rick", "Rico", "Ricky", and more. Richard is a common English, German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Catalan "Ricard" and the Italian "Riccardo", among others (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Andersen (other) * Richard Anderson (other) * Richard Cartwright (other) * Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudoscientist
Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claims; reliance on confirmation bias rather than rigorous attempts at refutation; lack of openness to evaluation by other experts; absence of systematic practices when developing hypotheses; and continued adherence long after the pseudoscientific hypotheses have been experimentally discredited. The demarcation between science and pseudoscience has scientific, philosophical, and political implications. Philosophers debate the nature of science and the general criteria for drawing the line between scientific theories and pseudoscientific beliefs, but there is general agreement on examples such as ancient astronauts, climate change denial, dowsing, evolution denial, Holocaust denialism, astrology, alchemy, alternative medicine, occultism, ufol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conspiracy Theorist
A conspiracy theory is an explanation for an event or situation that invokes a conspiracy by sinister and powerful groups, often political in motivation, when other explanations are more probable.Additional sources: * * * * The term has a negative connotation, implying that the appeal to a conspiracy is based on prejudice or insufficient evidence. A conspiracy theory is not the same as a conspiracy; instead, it refers to a hypothesized conspiracy with specific characteristics, such as an opposition to the mainstream consensus among those people (such as scientists or historians) who are qualified to evaluate its accuracy. Conspiracy theories resist falsification and are reinforced by circular reasoning: both evidence against the conspiracy and an absence of evidence for it are re-interpreted as evidence of its truth, whereby the conspiracy becomes a matter of faith rather than something that can be proven or disproven. Studies have linked belief in conspiracy theories to dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding the National Advisory Committee for Aeronautics (NACA), to give the U.S. space development effort a distinctly civilian orientation, emphasizing peaceful applications in space science. NASA has since led most American space exploration, including Project Mercury, Project Gemini, the 1968-1972 Apollo Moon landing missions, the Skylab space station, and the Space Shuttle. NASA supports the International Space Station and oversees the development of the Orion spacecraft and the Space Launch System for the crewed lunar Artemis program, Commercial Crew spacecraft, and the planned Lunar Gateway space station. The agency is also responsible for the Launch Services Program, which provides oversight of launch operations and countdown management f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyderabad, India
Hyderabad ( ; , ) is the capital and largest city of the Indian state of Telangana and the '' de jure'' capital of Andhra Pradesh. It occupies on the Deccan Plateau along the banks of the Musi River, in the northern part of Southern India. With an average altitude of , much of Hyderabad is situated on hilly terrain around artificial lakes, including the Hussain Sagar lake, predating the city's founding, in the north of the city centre. According to the 2011 Census of India, Hyderabad is the fourth-most populous city in India with a population of residents within the city limits, and has a population of residents in the metropolitan region, making it the sixth-most populous metropolitan area in India. With an output of 74 billion, Hyderabad has the fifth-largest urban economy in India. Muhammad Quli Qutb Shah established Hyderabad in 1591 to extend the capital beyond the fortified Golconda. In 1687, the city was annexed by the Mughals. In 1724, Asaf Jah I, th ... [...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] |
Motive (algebraic Geometry)
In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and crystalline cohomology. Philosophically, a "motif" is the "cohomology essence" of a variety. In the formulation of Grothendieck for smooth projective varieties, a motive is a triple (X, p, m), where ''X'' is a smooth projective variety, p: X \vdash X is an idempotent correspondence, and ''m'' an integer, however, such a triple contains almost no information outside the context of Grothendieck's category of pure motives, where a morphism from (X, p, m) to (Y, q, n) is given by a correspondence of degree n-m. A more object-focused approach is taken by Pierre Deligne in ''Le Groupe Fondamental de la Droite Projective Moins Trois Points''. In that article, a motive is a "system of realisations" – that is, a tupl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barry Mazur
Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in number theory, Mazur's torsion theorem in arithmetic geometry, the Mazur swindle in geometric topology, and the Mazur manifold in differential topology. Life Born in New York City, Mazur attended the Bronx High School of Science and MIT, although he did not graduate from the latter on account of failing a then-present ROTC requirement. He was nonetheless accepted for graduate studies at Princeton University, from where he received his PhD in mathematics in 1959 after completing a doctoral dissertation titled "On embeddings of spheres." He then became a Junior Fellow at Harvard University from 1961 to 1964. He is the Gerhard Gade University Professor and a Senior Fellow at Harvard. He is the brother of Joseph Mazur and the father of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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