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Karl Rubin
Karl Cooper Rubin (born January 27, 1956) is an American mathematician at University of California, Irvine as Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999. His research interest is in elliptic curves. He was the first mathematician (1986) to show that some elliptic curves over the rationals have finite Tate–Shafarevich groups. It is widely believed that these groups are always finite. Education and career Rubin graduated from Princeton University in 1976, and obtained his Ph.D. from Harvard in 1981. His thesis advisor was Andrew Wiles. He was a Putnam Fellow in 1974, and a Sloan Research Fellow in 1985. In 1988, Rubin received a National Science Foundation Presidential Young Investigator award, and in 1992 won the American Mathematical Society Cole Prize in number theory. In 2012 he became a fellow of the American Mathematical Society. Rubin's parents were mathemati ...
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Urbana, Illinois
Urbana ( ) is a city in and the county seat of Champaign County, Illinois, United States. As of the 2020 census, Urbana had a population of 38,336. As of the 2010 United States Census, Urbana is the 38th-most populous municipality in Illinois. It is included in the Champaign–Urbana metropolitan area. Urbana is notable for sharing the campus of the University of Illinois Urbana-Champaign with its twin city of Champaign. History The Urbana area was first settled by Europeans in 1822, when it was called "Big Grove".McGinty, Alice"The Story of Champaign-Urbana" Champaign Public Library When the county of Champaign was organized in 1833, the county seat was located on 40 acres of land, 20 acres donated by William T. Webber and 20 acres by Col. M. W. Busey, considered to be the city's founder, and the name "Urbana" was adopted after Urbana, Ohio, the hometown of State Senator John W. Vance, who authored the Enabling Act creating Champaign County. The creation of the new town was celeb ...
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Putnam Fellow
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as ''Putnam Fellows'') is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship), the top 100 individual scorers have their names mentioned in the American Mathematical Monthly (alphabetically ordered within rank), and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score ...
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Mathematics Genealogy Project
The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title (in its Mathematics Subject Classification), '' alma mater'', doctoral advisor, and doctoral students.. Origin of the database The project grew out of founder Harry Coonce's desire to know the name of his advisor's advisor.. Coonce was Professor of Mathematics at Minnesota State University, Mankato, at the time of the project's founding, and the project went online there in fall 1997.Mulcahy, Colm;The Mathematics Genealogy Project Comes of Age at Twenty-one(PDF) AMS Notices (May 2017) Coonce retired from Mankato in 1999, and in fall 2002 the university decided that it would no longer support the project. The project relocated at that time to North Dakota State U ...
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Stark Conjectures
In number theory, the Stark conjectures, introduced by and later expanded by , give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension ''K''/''k'' of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When ''K''/''k'' is an abelian extension and the order of vanishing of the L-function at ''s'' = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. and Cristian Dumitru Popescu gave extensions of this refined conjecture to higher orders of vanishing. Formulation The Stark conjectures, in the most general form, predict that the leading coefficient of an Artin L-function is the prod ...
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Euler System
In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles. Definition Although there are several definitions of special sorts of Euler system, there seems to be no published definition of an Euler system that covers all known cases. But it is poss ...
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Torus-based Cryptography
Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea was first introduced by Alice Silverberg and Karl Rubin in 2003 in the form of a public key algorithm by the name of CEILIDH. It improves on conventional cryptosystems by representing some elements of large finite fields compactly and therefore transmitting fewer bits. See also * Torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does n ... References * Karl Rubin, Alice Silverberg: Torus-Based Cryptography. CRYPTO 2003: 349–365 External links Torus-Based Cryptography— the paper introducing the concept (in PDF). Public-key cryptography {{Crypto-stub ...
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Judith Young (astronomer)
Judith Sharn Young (; September 15, 1952 – May 23, 2014) was an American physicist, astronomer, and educator. The American Physical Society honored Young with the first Maria Goeppert-Mayer Award for being the best young physicist in the world in 1986. Astronomer Nick Scoville of Caltech writes of her research: "Her pioneering galactic structure research included some of the earliest mapping of CO emission in galaxies followed by the most extensive surveys molecular gas and star formation in nearby galaxies." Career Young received her Bachelor of Arts degree in Astronomy from Harvard University and graduated with Honors. She received her M.S. and Ph.D. in physics from the University of Minnesota. Young began a postdoctoral fellowship at UMass in 1979, collaborating with Nick Z. Scoville in a study which measured the cold gas and carbon monoxide content of galaxies. The pair made the discovery that the distribution of light and gas is proportional in galaxies. The American A ...
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Vera Rubin
Vera Florence Cooper Rubin (; July 23, 1928 – December 25, 2016) was an American astronomer who pioneered work on galaxy rotation rates. She uncovered the discrepancy between the predicted and observed angular motion of galaxies by studying galactic rotation curves. Identifying the galaxy rotation problem, her work provided the first evidence for the existence of dark matter. These results were confirmed over subsequent decades. Beginning her academic career as the sole undergraduate in astronomy at Vassar College, Rubin went on to graduate studies at Cornell University and Georgetown University, where she observed deviations from Hubble flow in galaxies and provided evidence for the existence of galactic superclusters. She was honored throughout her career for her work, receiving the Bruce Medal, the Gold Medal of the Royal Astronomical Society, and the National Medal of Science, among others. Rubin spent her life advocating for women in science and was known for her ...
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Robert Joshua Rubin
Robert Joshua Rubin (; August 17, 1926 – January 18, 2008) was an American mathematician whose work involved modelling complex physical systems. He worked principally at the National Institute of Standards and Technology, National Bureau of Standards, and was a Fellow of the American Association for the Advancement of Science and also a Fellow of the American Physical Society. Education and career He received his bachelor's degree from Cornell University, and his doctorate also from Cornell, in 1951; his doctoral advisor was Peter Debye. He worked first at the Applied Physics Laboratory, Johns Hopkins Advanced Physics Laboratory, and then at the Bureau of Standards. Personal life From 1948 until his death in 2008, he was married to Vera Rubin. His children include Judith Young (astronomer) and Karl Rubin (mathematician). References

{{DEFAULTSORT:Rubin, Robert Joshua 1926 births 2008 deaths Cornell University alumni Fellows of the American Association for the ...
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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 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 analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic object ...
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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 i ...
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