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Rostislav Grigorchuk
Rostislav Ivanovich Grigorchuk ( ua, Ростисла́в Iва́нович Григорчу́к; b. February 23, 1953) is a mathematician working in different areas of mathematics including group theory, dynamical systems, geometry and computer science. He holds the rank of Distinguished Professor in the Mathematics Department of Texas A&M University. Grigorchuk is particularly well known for having constructed, in a 1984 paper, the first example of a finitely generated group of intermediate growth, thus answering an important problem posed by John Milnor in 1968. This group is now known as the Grigorchuk groupPierre de la Harpe. ''Topics in geometric group theory.'' Chicago Lectures in Mathematics. University of Chicago Press, Chicago. and it is one of the important objects studied in geometric group theory, particularly in the study of branch groups, automaton groups and iterated monodromy groups. Grigorchuk is one of the pioneers of asymptotic group theory as well as of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vyshnivets
Vyshnivets ( uk, Вишнівець, translit. ''Vyshnivets’''; pl, Wiśniowiec) is an urban-type settlement in Kremenets Raion (district) of the Ternopil Oblast (province) of western Ukraine. It hosts the administration of Vyshnivets settlement hromada, one of the hromadas of Ukraine. Population: Vyshnivets is better known as a family estate of the Polish royal house of Wiśniowiecki (originally Ruthenian princes), which is known for switching from Eastern Orthodoxy to Catholicism (as part of Polonization) as well as the Cossack Hetman Dmytro "Baida" Vyshnevetsky, who established the first Zaporizhian Sich on the island of Small (Mala) Khortytsia on the Dnipro River in 1552 in defense of the lands. History Early History, to 1939 The area was first mentioned in 1395 soon after annexation of the Kingdom of Galicia-Volhynia by the Kingdom of Poland when the first defensive castle was constructed in the area by Dmytro Korybut who had acquired the land from Great Prince Vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professors In The United States
Professors in the United States commonly occupy any of several positions of teaching and research within a college or university. In the U.S., the word "professor" informally refers collectively to the academic ranks of assistant professor, associate professor, or professor. This usage differs from the predominant usage of the word professor internationally, where the unqualified word professor only refers to "full professors." The majority of university lecturers and instructors in the United States, , do not occupy these tenure-track ranks, but are part-time adjuncts, or more commonly referred as college teachers. Research and education are among the main tasks of tenured and tenure-track professors, with the amount of time spent on research or teaching depending strongly on the type of institution. Publication of articles in conferences, journals, and books is essential to occupational advancement. As of August 2007, teaching in tertiary educational institutions is one of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious university in the country. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches (including five foreign ones in the Commonwealth of Independent States countries). Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner had been affiliated with the university. The university was ranked 18th by ''The Three University Missions Ranking'' in 2022, and 76th by the ''QS World University Rankings'' in 2022, #293 in the world by the global ''Times Higher World University Rankings'', and #326 by ''U.S. News & World Report'' in 2022. It was the highest-ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev ( Ukrainian SSR), Minsk ( Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Gove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Graph Theory
In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally diagonalizable; its eigenvalues are real algebraic integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdière number. Cospectral graphs Two graphs are called cospectral or isospectral if the adjacency matrices of the graphs are isospectral, that is, if the adjacency matrices have equal multisets of eigenvalues. Cospectral graphs need not be isomorphic, but isomorphic graphs a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), 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 homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphere i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterated Monodromy Group
In geometric group theory and dynamical systems the iterated monodromy group of a covering map is a group describing the monodromy action of the fundamental group on all iterations of the covering. A single covering map between spaces is therefore used to create a tower of coverings, by placing the covering over itself repeatedly. In terms of the Galois theory of covering spaces, this construction on spaces is expected to correspond to a construction on groups. The iterated monodromy group provides this construction, and it is applied to encode the combinatorics and symbolic dynamics of the covering, and provide examples of self-similar groups. Definition The iterated monodromy group of ''f'' is the following quotient group: :\mathrmf := \frac where : *f:X_1\rightarrow X is a covering of a path-connected and locally path-connected topological space ''X'' by its subset X_1, * \pi_1 (X, t) is the fundamental group of ''X'' and * \digamma :\pi_1 (X, t)\rightarrow \mathrm\,f^(t) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Igor Pak
Igor Pak (russian: link=no, Игорь Пак) (born 1971, Moscow, Soviet Union) is a professor of mathematics at the University of California, Los Angeles, working in combinatorics and discrete probability. He formerly taught at the Massachusetts Institute of Technology and the University of Minnesota, and he is best known for his bijective proof of the Young tableau#Dimension of a representation, hook-length formula for the number of Young tableaux, and his work on random walks. He was a keynote speaker alongside George Andrews (mathematician), George Andrews and Doron Zeilberger at the 2006 Harvey Mudd College Mathematics Conference on Enumerative Combinatorics. Pak is an Associate Editor for the journal Discrete Mathematics (journal), ''Discrete Mathematics''. He gave a László Fejes Tóth, Fejes Tóth Lecture at the University of Calgary in February 2009. In 2018, he was an List of International Congresses of Mathematicians Plenary and Invited Speakers#2018, Rio de Janeiro, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rendiconti Del Circolo Matematico Di Palermo
The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.The Mathematical Circle of Palermo . Retrieved 2011-06-19. It began accepting foreign members in 1888, and by the time of Guccia's death in 1914 it had become the foremost international mathematical society, with approximately one thousand members. However, subsequently to that time it declined in influence. Publications ''Rendiconti del Circolo Matemat ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
