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József Solymosi
József Solymosi is a Hungarian-Canadian mathematician and a professor of mathematics at the University of British Columbia. His main research interests are arithmetic combinatorics, discrete geometry, graph theory, and combinatorial number theory. Education and career Solymosi earned his master's degree in 1999 under the supervision of László Székely from the Eötvös Loránd University and his Ph.D. in 2001 at ETH Zürich under the supervision of Emo Welzl. His doctoral dissertation was ''Ramsey-Type Results on Planar Geometric Objects''. From 2001 to 2003 he was S. E. Warschawski Assistant Professor of Mathematics at the University of California, San Diego. He joined the faculty of the University of British Columbia in 2002. He was editor in chief of the ''Electronic Journal of Combinatorics'' from 2013 to 2015. Contributions Solymosi was the first online contributor to the first Polymath Project, set by Timothy Gowers to find improvements to the Hales–Jewett theorem. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oberwolfach Research Institute For Mathematics
The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that time was clearly failing. The location was selected to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timothy Gowers
Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics. Education Gowers attended King's College School, Cambridge, as a choirboy in the choir of King's College, Cambridge, King's College choir, and then Eton College as a King's Scholar, where he was taught mathematics by Norman Routledge. In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score. He completed his PhD, with a dissertation on ''Symmetric Structures in Banach Spaces'' at Trinity College, Cambridge in 1990, supervised by Béla Bollobás. Career and research After his PhD, Gowers was elected to a Junior Research Fellowship at Trinity College. From 1991 until his return to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aisenstadt Prize
The André Aisenstadt Prize recognizes a young Canadian mathematician's outstanding achievement in pure or applied mathematics. It has been awarded annually since 1992 (except in 1994, when no prize was given) by the Centre de Recherches Mathématiques at the University of Montreal. The prize consists of a $3,000 award and a medal. It is named after . Prize winners Source * 2025 Carlo Pagano(Concordia University) * 2024 Alexander Kupers (University of Toronto Scarborough) * 2023 Elina Robeva (University of British Columbia) and Yakov Shlapentokh-Rothman (University of Toronto) * 2022 Yevgeny Liokumovich (University of Toronto) * 2021 Giulio Tiozzo (University of Toronto) and Tristan C. Collins (Massachusetts Institute of Technology) * 2020 Robert Haslhofer (University of Toronto) and Egor Shelukhin (Université de Montréal) * 2019 Yaniv Plan (University of British Columbia) * 2018 Benjamin Rossman (University of Toronto) * 2017 Jacob Tsimerman (University of Toronto) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sloan Research Fellowship
The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. Fellowships were initially awarded in physics, chemistry, and mathematics. Awards were later added in neuroscience (1972), economics (1980), computer science (1993), computational and evolutionary molecular biology (2002), and ocean sciences or earth systems sciences (2012). Winners of these two-year fellowships are awarded $75,000, which may be spent on any expense supporting their research. From 2012 through 2020, the foundation awarded 126 research fellowship each year; in 2021, 128 were awarded, and 118 were awarded in 2022. Eligibility and selection To be eligible, a candidate must hold a Ph.D. or equivalent degree and must be a member of the faculty of a college, university, or other degree-granting institution in the United Sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős Distinct Distances Problem
In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015. The conjecture In what follows let denote the minimal number of distinct distances between points in the plane, or equivalently the smallest possible cardinality of their distance set. In his 1946 paper, Erdős proved the estimates :\sqrt-1/2\leq g(n)\leq c n/\sqrt for some constant c. The lower bound was given by an easy argument. The upper bound is given by a \sqrt\times\sqrt square grid. For such a grid, there are O( n/\sqrt) numbers below ''n'' which are sums of two squares, expressed in big O notation; see Landau–Ramanujan constant. Erdős conjectured that the upper bound was closer to the true value of ''g''(''n''), and specifically that (using big Omega notation) g(n) = \Omega(n^c) holds for every . Partial results Paul Erdős' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Szemerédi Theorem
In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of the sets and (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants and such that, for any non-empty set , :\max( , A+A, , , A \cdot A, ) \geq c , A, ^ . It was proved by Paul Erdős and Endre Szemerédi in 1983.. The notation denotes the cardinality of the set . The set of pairwise sums is and is called the sumset of . The set of pairwise products is and is called the product set of ; it is also written . The theorem is a version of the maxim that additive structure and multiplicative structure cannot coexist. It can also be viewed as an assertion that the real line does not contain any set resembling a finite subring or finite subfield; it is the first example of what is now known as the sum-product phenomenon, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Plane
In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows for a geometric interpretation of complex numbers. Under addition, they add like vector (geometry), vectors. The multiplication of two complex numbers can be expressed more easily in polar coordinates: the magnitude or ' of the product is the product of the two absolute values, or moduli, and the angle or ' of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. Notational conventions Complex numbers In complex analysis, the complex numbers are customarily represented by the symbol , which can be sepa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Szemerédi–Trotter Theorem
The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (''i.e.'', the number of point-line pairs, such that the point lies on the line) is O \left ( n^ m^ + n + m \right ). This bound cannot be improved, except in terms of the implicit constants in its big O notation. An equivalent formulation of the theorem is the following. Given points and an integer , the number of lines which pass through at least of the points is O \left( \frac + \frac \right ). The original proof of Endre Szemerédi and William T. Trotter was somewhat complicated, using a combinatorial technique known as '' cell decomposition''. Later, László Székely discovered a much simpler proof using the crossing number inequality for graphs. This method has been used to produce the explicit upper bound 2.5n^ m^ + n + m on the number of incidences. Subsequent research has lowered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Tao
Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory. Tao was born to Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014, and is a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers, and is widely regarded as one of the greatest living mathematicians. Life and career Family Tao's parents are first generation immigrants from Hong Kong to Australia.'' Wen Wei Po'', Page A4, 24 August ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zariski Topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly used in real or complex analysis; in particular, it is not Hausdorff. This topology was introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a topological space. The Zariski topology allows tools from topology to be used to study algebraic varieties, even when the underlying field is not a topological field. This is one of the basic ideas of scheme theory, which allows one to build general algebraic varieties by gluing together affine varieties in a way similar to that in manifold theory, where manifolds are built by gluing together charts, which are open subsets of real affine spaces. The Zariski topology of an algebraic variety is the topology whose closed sets are the algebraic subsets of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Ulam Problem
In mathematics, the Erdős–Ulam problem asks whether the plane contains a dense set of points whose Euclidean distances are all rational numbers. It is named after Paul Erdős and Stanislaw Ulam. Large point sets with rational distances The Erdős–Anning theorem states that a set of points with integer distances must either be finite or lie on a single line. However, there are other infinite sets of points with rational distances. For instance, on the unit circle, let ''S'' be the set of points :(\cos\theta,\sin\theta) where \theta is restricted to values that cause \tan\tfrac to be a rational number. For each such point, both \sin\tfrac and \cos\tfrac\theta 2 are themselves both rational, and if \theta and \varphi define two points in ''S'', then their distance is the rational number : \left, 2\sin\frac \theta 2 \cos\frac \varphi 2 -2\sin\frac \varphi 2 \cos\frac \theta 2 \. More generally, a circle with radius \rho contains a dense set of points at rational distances to ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Anning Theorem
The Erdős–Anning theorem states that, whenever an Infinite set, infinite number of points in the plane all have integer distances, the points lie on a straight line. The same result holds in higher dimensional Euclidean spaces. The theorem cannot be strengthened to give a finite bound on the number of points: there exist arbitrarily large finite sets of points that are not on a line and have integer distances. The theorem is named after Paul Erdős and Norman H. Anning, who published a proof of it in 1945. Erdős later supplied a simpler proof, which can also be used to check whether a point set forms an Erdős–Diophantine graph, an inextensible system of integer points with integer distances. The Erdős–Anning theorem inspired the Erdős–Ulam problem on the existence of dense set, dense point sets with rational distances. Rationality versus integrality Although there can be no infinite non-Collinearity, collinear set of points with integer distances, there are infini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
