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Andrew Ogg
Andrew Pollard Ogg (born April 9, 1934, Bowling Green, Ohio) is an American mathematician, a professor emeritus of mathematics at the University of California, Berkeley. Education Ogg was a student at Bowling Green State University in the mid 1950s. Ogg received his Ph.D. in 1961 from Harvard University under the supervision of John Tate. Career Ogg worked in algebra and number theory. His accomplishments include the Grothendieck–Ogg–Shafarevich formula, Ogg's formula for the conductor of an elliptic curve, the Néron–Ogg–Shafarevich criterion and the 1975 characterization of supersingular primes, the starting point for the theory of monstrous moonshine. He also posed the torsion conjecture In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in ter ... in 1973 and is the author of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Ogg
Andrew Pollard Ogg (born April 9, 1934, Bowling Green, Ohio) is an American mathematician, a professor emeritus of mathematics at the University of California, Berkeley. Education Ogg was a student at Bowling Green State University in the mid 1950s. Ogg received his Ph.D. in 1961 from Harvard University under the supervision of John Tate. Career Ogg worked in algebra and number theory. His accomplishments include the Grothendieck–Ogg–Shafarevich formula, Ogg's formula for the conductor of an elliptic curve, the Néron–Ogg–Shafarevich criterion and the 1975 characterization of supersingular primes, the starting point for the theory of monstrous moonshine. He also posed the torsion conjecture In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in ter ... in 1973 and is the author of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monstrous Moonshine
In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group ''M'' and modular functions, in particular, the ''j'' function. The term was coined by John Conway and Simon P. Norton in 1979. The monstrous moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, which has the monster group as its group of symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac–Moody algebras. History In 1978, John McKay found that the first few ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Bowling Green, Ohio
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theorists
A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic identity * Religious group (other), a group whose members share the same religious identity * Social group, a group whose members share the same social identity * Tribal group, a group whose members share the same tribal identity * Organization, an entity that has a collective goal and is linked to an external environment * Peer group, an entity of three or more people with similar age, ability, experience, and interest Social science * In-group and out-group * Primary, secondary, and reference groups * Social group * Collectives Science and technology Mathematics * Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions Chemistry * Functional group, a group of atoms which provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Alumni
The list of Harvard University people includes notable graduates, professors, and administrators affiliated with Harvard University. For a list of notable non-graduates of Harvard, see notable non-graduate alumni of Harvard. For a list of Harvard's presidents, see President of Harvard University. Eight President of the United States, Presidents of the United States have graduated from Harvard University: John Adams, John Quincy Adams, Rutherford B. Hayes, John F. Kennedy, Franklin Delano Roosevelt, Theodore Roosevelt, George W. Bush, and Barack Obama. Bush graduated from Harvard Business School, Hayes and Obama from Harvard Law School, and the others from Harvard College. Over 150 Nobel Prize winners have been associated with the university as alumni, researchers or faculty. Nobel laureates Pulitzer Prize winners ... [...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] |
1934 Births
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * January 26 – A 10-year German–Polish declaration of non-aggression is signed by Nazi Germany and the Second Polish Republic. * January 30 ** In Nazi Germany, the political power of federal states such as Prussia is substantially abolished, by the "Law on the Reconstruction of the Reich" (''Gesetz über den Neuaufbau des Reiches''). ** Franklin D. Roosevelt, President of the United States, signs the Gold Reserve Act: all gold held in the Federal Reserve is to be surrendered to the United States Department of the Treasury; immediately following, the President raises the statutory gold price from US$20.67 per ounce to $35. * February 6 – F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsion Conjecture
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of elliptic curves. Elliptic curves From 1906 to 1911, Beppo Levi published a series of papers investigating the possible finite orders of points on elliptic curves over the rationals. He showed that there are infinitely many elliptic curves over the rationals with the following torsion groups: * ''C''''n'' with 1 ≤ ''n'' ≤ 10, where ''C''''n'' denotes the cyclic group of order ''n''; * ''C''12; * ''C''2n × ''C''2 with 1 ≤ ''n'' ≤ 4, where × denotes the direct sum. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersingular Prime (moonshine Theory)
In the mathematical branch of moonshine theory, a supersingular prime is a prime number that divides the order of the Monster group ''M'', which is the largest sporadic simple group. There are precisely fifteen supersingular prime numbers: the first eleven primes ( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31), as well as 41, 47, 59, and 71. The non-supersingular primes are 37, 43, 53, 61, 67, and any prime number greater than or equal to 73. Supersingular primes are related to the notion of supersingular elliptic curves as follows. For a prime number ''p'', the following are equivalent: # The modular curve ''X''0+(''p'') = ''X''0(''p'') / ''w''p, where ''w''p is the Fricke involution of ''X''0(''p''), has genus zero. # Every supersingular elliptic curve in characteristic ''p'' can be defined over the prime subfield F''p''. # The order of the Monster group is divisible by ''p''. The equivalence is due to Andrew Ogg. More precisely, in 1975 Ogg showed that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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