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Von Neumann Conjecture
In mathematics, the von Neumann conjecture stated that a group (mathematics), group ''G'' is non-Amenable group, amenable if and only if ''G'' contains a subgroup that is a free group on two Generating set of a group, generators. The conjecture was disproved in 1980. In 1929, during his work on the Banach–Tarski paradox, John von Neumann defined the concept of amenable groups and showed that no amenable group contains a free subgroup of rank 2. The suggestion that the converse might hold, that is, that every non-amenable group contains a free subgroup on two generators, was made by a number of different authors in the 1950s and 1960s. Although von Neumann's name is popularly attached to the conjecture, its first written appearance seems to be due to Mahlon Marsh Day in 1957. The Tits alternative is a fundamental theorem which, in particular, establishes the conjecture within the class of linear groups. The historically first potential counterexample is Thompson groups, Thompson g ... [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Adian
Sergei Ivanovich Adian, also Adyan ( hy, Սերգեյ Իվանովիչ Ադյան; russian: Серге́й Ива́нович Адя́н; 1 January 1931 – 5 May 2020), 4381, and hence for all multiples of those odd integers as well. The solution of the Burnside problem was certainly one of the most outstanding and deep mathematical results of the past century. At the same time, this result is one of the hardest theorems: just the inductive step of a complicated induction used in the proof took up a whole issue of volume 32 of Izvestiya, even lengthened by 30 pages. In many respects the work was literally carried to its conclusion by the exceptional persistence of Adian. In that regard it is worth recalling the words of Novikov, who said that he had never met a mathematician more ‘penetrating’ than Adian. In contrast to the Adian–Rabin theorem, the paper of Adian and Novikov in no way ‘closed’ the Burnside problem. Moreover, over a long period of more than ten years Adi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disproved Conjectures
A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition. In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and from other previously established theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In some areas of epistemology and theology, the notion of justification plays approximately the role of proof, while in jurisprudence the corresponding term is evidence, with "burden of proof" as a concept common to bot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Groups
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Topology
The ''Journal of Topology'' is a peer-reviewed scientific journal which publishes papers of high quality and significance in topology, geometry, and adjacent areas of mathematics. It was established in 2008, when the Editorial Board of ''Topology'' resigned due to the increasing costs of Elsevier's subscriptions. The journal is owned and managed by the London Mathematical Society and produced, distributed, sold and marketed by John Wiley & Sons. It appears quarterly with articles published individually online prior to appearing in a printed issue. Editorial Board * Arthur Bartels (University of Münster) * Andrew Blumberg (University of Texas at Austin) * Jeffrey Brock (Yale University) * Simon Donaldson (Imperial College London) * Cornelia Druţu Badea (University of Oxford) * Mark Gross (University of Cambridge) * Lars Hesselholt (University of Copenhagen) * Misha Kapovich (UC Davis) *Frances Kirwan (University of Oxford) * Marc Lackenby (University of Oxford) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groups, Geometry, And Dynamics
''Groups, Geometry, and Dynamics'' is a quarterly peer-reviewed mathematics journal published quarterly by the European Mathematical Society. It was established in 2007 and covers all aspects of groups, group actions, geometry and dynamical systems. The journal is indexed by '' Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.65, and its 2012 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... is 0.867. External links * Mathematics journals Academic journals established in 2007 English-language journals European Mathematical Society academic journals Quarterly journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The National Academy Of Sciences Of The United States Of America
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2021 impact factor of 12.779. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the mass media, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open access journal, with an embargo period of six months that can be bypassed for an author fee (hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Publications Mathématiques De L'IHÉS
''Publications Mathématiques de l'IHÉS'' is a peer-reviewed mathematical journal. It is published by Springer Science+Business Media on behalf of the Institut des Hautes Études Scientifiques, with the help of the Centre National de la Recherche Scientifique. The journal was established in 1959 and was published at irregular intervals, from one to five volumes a year. It is now biannual. The editor-in-chief is Claire Voisin (Collège de France). See also *''Annals of Mathematics'' *''Journal of the American Mathematical Society'' *''Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editor ...'' External links * Back issues from 1959 to 2010 Mathematics journals Publications established in 1959 Springer Science+Business Media academic journals Biannual journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finiteness Properties Of Groups
In mathematics, finiteness properties of a group are a collection of properties that allow the use of various algebraic and topological tools, for example group cohomology, to study the group. It is mostly of interest for the study of infinite groups. Special cases of groups with finiteness properties are finitely generated and finitely presented groups. Topological finiteness properties Given an integer ''n'' ≥ 1, a group \Gamma is said to be ''of type'' ''F''''n'' if there exists an aspherical CW-complex whose fundamental group is isomorphic to \Gamma (a classifying space for \Gamma) and whose ''n''-skeleton is finite. A group is said to be of type ''F''∞ if it is of type ''F''''n'' for every ''n''. It is of type ''F'' if there exists a finite aspherical CW-complex of which it is the fundamental group. For small values of ''n'' these conditions have more classical interpretations: * a group is of type ''F''1 if and only if it is finitely generated (the rose w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Justin T
Justin may refer to: People * Justin (name), including a list of persons with the given name Justin * Justin (historian), a Latin historian who lived under the Roman Empire * Justin I (c. 450–527), or ''Flavius Iustinius Augustus'', Eastern Roman Emperor who ruled from 518 to 527 * Justin II (c. 520–578), or ''Flavius Iustinius Iunior Augustus'', Eastern Roman emperor who ruled from 565 to 578 * Justin (magister militum per Illyricum) (''fl.'' 538–552), a Byzantine general * Justin (Moesia), a Byzantine general killed in battle in 528 * Justin (consul 540) (c. 525–566), a Byzantine general * Justin Martyr (103–165), a Christian martyr * Justin (gnostic), 2nd-century Gnostic Christian; sometimes confused with Justin Martyr * Justin the Confessor (d 269) * Justin of Chieti, venerated as an early bishop of Chieti, Italy * Justin of Siponto (c. 4th century), venerated as Christian martyrs by the Catholic Church * Justin de Jacobis (1800–1860), an Italian Lazarist mission ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolas Monod
Nicolas Monod is a professor at École Polytechnique Fédérale de Lausanne (EPFL) and known for work on bounded cohomology, ergodic theory, geometry ( CAT(0) spaces), locally compact groups and amenability. He was born in Montreux, Switzerland. He obtained his PhD from ETH Zurich in 2001 with thesis "Continuous Bounded Cohomology of Locally Compact Groups" written under the direction of Marc Burger. Career Monod is a Fellow of the American Mathematical Society. He has been awarded the Gauss Lectureship and the Berwick Prize, and was an invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ... in 2006. He was one of the youngest Advanced Investigator awardees in the history of the European Research Council. Monod was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Sapir
Mark Sapir (February 12, 1957 - October 8, 2022)Mark Sapir's CV Department of Mathematics, . Accessed November 4, 2018Mark Sapir Obituary Accessed October 10, 2022 was a U.S. and Russian mathematician working in , |
