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Oleg Izhboldin
Oleg Tomovich Izhboldin (russian: Олег Томович Ижболдин; 1963 - 2000) was a Russian mathematician who was first to provide a non-trivial example of an odd u-invariant field solving a classical Kaplansky's conjecture. Oleg Izhboldin graduated from the 45th Physics-Mathematics School in Saint Petersburg, then from the Faculty of Mathematics and Mechanics of Leningrad State University. He received his Ph.D. from the same University in 1988 and Doktor nauk degree in 2000. According to Alexander Merkurjev: ''Oleg found his niche in algebra, namely, the algebraic theory of quadratic forms. ... This needed knowledge in different areas of mathematics was especially important in light of the recently discovered interaction (by Oleg, among others) between the theory of quadratic forms and various branches of mathematics that had seemed absolutely unrelated before... Oleg mastered the algebraic theory of quadratic form In mathematics, a quadratic form is a polynomia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
U-invariant
In mathematics, the universal invariant or ''u''-invariant of a field describes the structure of quadratic forms over the field. The universal invariant ''u''(''F'') of a field ''F'' is the largest dimension of an anisotropic quadratic space over ''F'', or ∞ if this does not exist. Since formally real fields have anisotropic quadratic forms (sums of squares) in every dimension, the invariant is only of interest for other fields. An equivalent formulation is that ''u'' is the smallest number such that every form of dimension greater than ''u'' is isotropic, or that every form of dimension at least ''u'' is universal. Examples * For the complex numbers, ''u''(C) = 1. * If ''F'' is quadratically closed then ''u''(''F'') = 1. * The function field of an algebraic curve over an algebraically closed field has ''u'' ≤ 2; this follows from Tsen's theorem that such a field is quasi-algebraically closed.Lam (2005) p.376 * If ''F'' is a non-real global or local field, or more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaplansky's Conjectures
The mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures on Hopf algebras. They are usually known as Kaplansky's conjectures. Group rings Let be a field, and a torsion-free group. Kaplansky's ''zero divisor conjecture'' states: * The group ring does not contain nontrivial zero divisors, that is, it is a domain. Two related conjectures are known as, respectively, Kaplansky's ''idempotent conjecture'': * does not contain any non-trivial idempotents, i.e., if , then or . and Kaplansky's ''unit conjecture'' (which was originally made by Graham Higman and popularized by Kaplansky): * does not contain any non-trivial units, i.e., if in , then for some in and in . The zero-divisor conjecture implies the idempotent conjecture and is implied by the unit conjecture. As of 2021, the zero divisor and idempotent conjectures are open. The unit conjecture, however, was disproved for fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
45th Physics-Mathematics School
Dmitry Konstantinovich Faddeev Academic Gymnasium at Saint Petersburg State University (russian: Академическая гимназия имени Д. К. Фаддеева Санкт-Петербургского государственного университета) also known as the 45th Physics Mathematics School (russian: 45-ая Физико-математическая школа) is a selective secondary boarding school at the Saint Petersburg State University established in 1963 in what was then the Soviet Union, now Russia. In 2015 it was named after Russian mathematician Dmitry Konstantinovich Faddeev, who was one of the founders of the school. History Boarding School No 45 The boarding school with physics-mathematics and chemistry-biology specialization was organized by the decree of Council of Ministers of the Soviet Union No 905 (23 August 1963) "On organization of specialized boarding schools with the physics-mathematics and chemistry-biology profiles" The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), is the second-largest city in Russia. It is situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, with a population of roughly 5.4 million residents. Saint Petersburg is the fourth-most populous city in Europe after Istanbul, Moscow and London, the most populous city on the Baltic Sea, and the world's northernmost city of more than 1 million residents. As Russia's Imperial capital, and a historically strategic port, it is governed as a federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the site of a captured Swedish fortress, and was named after apostle Saint Peter. In Russia, Saint Petersburg is historically and culturally associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg State University
Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the Great, the university from the beginning has had a focus on fundamental research in science, engineering and humanities. During the Soviet period, it was known as Leningrad State University (russian: Ленинградский государственный университет). It was renamed after Andrei Zhdanov in 1948 and was officially called "Leningrad State University, named after A. A. Zhdanov and decorated with the Order of Lenin and the Order of the Red Banner of Labour." Zhdanov's was removed in 1989 and Leningrad in the name was officially replaced with Saint Petersburg in 1992. It is made up of 24 specialized faculties (departments) and institutes, the Academic Gymnasium, the Medical College, the College of Physical Culture ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doktor Nauk
Doctor of Sciences ( rus, доктор наук, p=ˈdoktər nɐˈuk, abbreviated д-р наук or д. н.; uk, доктор наук; bg, доктор на науките; be, доктар навук) is a higher doctoral degree in the Russian Empire, Soviet Union and many post-Soviet countries, which may be earned after the Candidate of Sciences. History The "Doctor of Sciences" degree was introduced in the Russian Empire in 1819 and abolished in 1917. Later it was revived in the USSR on January 13, 1934, by a decision of the Council of People's Commissars of the USSR. By the same decision, a lower degree, "Candidate of Sciences" (''kandidat nauk''), roughly the Russian equivalent to the research doctorate in other countries, was first introduced. This system was generally adopted by the USSR/Russia and many post-Soviet/Eastern bloc states, including Bulgaria, Belarus, former Czechoslovakia, Poland (since abolished), and Ukraine. But note that the former Yugoslav degree "Do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Merkurjev
Aleksandr Sergeyevich Merkurjev (russian: Алекса́ндр Сергее́вич Мерку́рьев, born September 25, 1955) is a Russian-American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles. Work Merkurjev's work focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980s Merkurjev proved a fundamental result about the structure of central simple algebras of period dividing 2, which relates the 2-torsion of the Brauer group with Milnor K-theory. In subsequent work with Suslin this was extended to higher torsion as the Merkurjev–Suslin theorem. The full statement of the norm residue isomorphism theorem (also known as the Bloch-Kato conjecture) was proven by Voevodsky. In the late 1990s Merkurjev gave the most general approach to the notion of essential dimension, introduced by Buhler and R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over . If K=\mathbb R, and the quadratic form takes zero only when all variables are simultaneously zero, then it is a definite quadratic form, otherwise it is an isotropic quadratic form. Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric, second fundamental form), differential topology ( intersection forms of four-manifolds), and Lie theory (the Killing form). Quadratic forms are not to be confused with a quadratic equation, which has only one variable and includes terms of degree two or less. A quadratic form is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called the capital of the world. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the region France's primate city. The Paris Region had a GDP of €739 billion ($743 billion) in 2019, which is the highest in Europe. According to the Economist Intelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians From Saint Petersburg
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 Hypatia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg State University Alumni
In religious belief, a saint is a person who is recognized as having an exceptional degree of holiness, likeness, or closeness to God. However, the use of the term ''saint'' depends on the context and denomination. In Catholic, Eastern Orthodox, Anglican, Oriental Orthodox, and Lutheran doctrine, all of their faithful deceased in Heaven are considered to be saints, but some are considered worthy of greater honor or emulation. Official ecclesiastical recognition, and consequently a public cult of veneration, is conferred on some denominational saints through the process of canonization in the Catholic Church or glorification in the Eastern Orthodox Church after their approval. While the English word ''saint'' originated in Christianity, historians of religion tend to use the appellation "in a more general way to refer to the state of special holiness that many religions attribute to certain people", referring to the Jewish tzadik, the Islamic walī, the Hindu rishi or Sikh g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
