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Clay Research Award
__NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievements in mathematical research. The following mathematicians have received the award: See also * List of mathematics awards This list of mathematics awards contains articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the world. Som ... External links Official web page {{Webarchive, url=https://web.archive.org/web/20180111180359/http://ww ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Vlad Vicol
Vlad is a Romanian male name. It is more commonly a nativized hypocorism of Vladislav and can also be used as a surname. Alternately, it may be a hypocoristic form of the Slavic name ''Vladimir'' (although the normative nickname is Vova). It may refer to: Given name People * Vlad I of Wallachia (), ''voivode'' (prince) of Wallachia * Vlad II Dracul (before 1395 – 1448), ''voivode'' of Wallachia * Vlad the Impaler (1428/31 – 1476/77), ''voivode'' of Wallachia as Vlad III, inspiration for the character Count Dracula * Vlad Călugărul (before 1425? – 1495), ''voivode'' of Wallachia as Vlad IV, half-brother of Vlad the Impaler * Vlad cel Tânăr (1494–1512), ''voivode'' of Wallachia as Vlad V * Vlad VI Înecatul (c. 1508 – 1532), ''voivode'' of Wallachia * Vlad Vintilă de la Slatina (died 1535), ''voivode'' of Wallachia as Vlad VII * Vlad Achim (born 1989), Romanian footballer * Vlad Bădălicescu (born 1988), Romanian rugby union footballer * Vl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
Nets Katz
Nets Hawk Katz is the W.L. Moody Professor of Mathematics at Rice University. He was a professor of mathematics at Indiana University Bloomington until March 2013 and the IBM Professor of Mathematics at the California Institute of Technology until 2023. He is currently the W. L. Moody Professor of Mathematics at Rice University. Katz earned a B.A. in mathematics from Rice University in 1990 at the age of 17. He received his Ph.D. in 1993 under Dennis DeTurck at the University of Pennsylvania, with a dissertation titled "Noncommutative Determinants and Applications". He is the author of several important results in combinatorics (especially additive combinatorics), harmonic analysis and other areas. In 2003, jointly with Jean Bourgain and Terence Tao, he proved that any subset of \Z/p\Z grows substantially under either addition or multiplication. More precisely, if A is a set such that \max(, A \cdot A, , , A+A, ) \leq K, A, , then A has size at most K^C or at least p/K^C where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Larry Guth
Lawrence David Guth (; born 1977) is a professor of mathematics at the Massachusetts Institute of Technology. Education and career Guth graduated from Yale University in 2000 with a BS in mathematics. In 2005, he received his PhD in mathematics from the Massachusetts Institute of Technology (MIT), where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka. After MIT, Guth went to Stanford as a postdoc and later to the University of Toronto as an assistant professor on a tenure track In 2011, New York University's Courant Institute of Mathematical Sciences hired Guth as a professor, listing his areas of interest as "metric geometry, harmonic analysis, and geometric combinatorics." In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics. Research In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds and, along with Nets Katz, found a solution to the Erdős distinct distances ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrix (mathematics), matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The algebraic objects amenable to such a description include group (mathematics), groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the group representation, representation theory of groups, in which elements of a group are represented by invertible matrices such that the group operation is matrix multiplication. Representation theory is a useful method because it reduces problems in abstract algebra to problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mirror Symmetry (string Theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometry, geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geordie Williamson
Geordie Williamson (born 1981 in Bowral, Australia) is an Australian mathematician at the University of Sydney. He became the youngest living Fellow of the Royal Society when he was elected in 2018 at the age of 36. Education Educated at Chevalier College, Williamson graduated in 1999 with a University Admission Index, UAI of 99.45. He studied at the University of Sydney and graduated with a Bachelor's degree in 2003 and then at the University of Freiburg, Albert-Ludwigs University of Freiburg, where he received his doctorate in 2008 under the supervision of Wolfgang Soergel. Williamson is the brother of the late James Williamson (Australian cyclist), James Williamson, a World Solo 24-hour mountain bike champion who died while competing in South Africa in 2010. Research and career After his PhD, Williamson was a post-doctoral researcher at the University of Oxford, based at St. Peter's College, Oxford, and from 2011 until 2016 he was at the Max Planck Institute for Mathematics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bernd Siebert
Bernd Siebert (born 5 March 1964 in Berlin-Wilmersdorf) is a German mathematician who researches in algebraic geometry. Life Siebert studied mathematics starting 1984 at the University of Erlangen. In 1986, he changed to the University of Bonn and in 1987 to the University of Göttingen where he finished his Diplom in 1989 under the supervision of Hans Grauert with distinction. He became Grauert's PhD student and assistant in Göttingen. He received his PhD in 1992 (''Faserzykelräume, geometrische Plattifikation und meromorphe Äquivalenzrelationen''). A stay at the Courant Institute followed in 1993–94 after which we went to Bochum. In 1997–98 he spent some time at the MIT as a visiting scholar before completing his habilitation in Bochum in 1998 (''Gromov–Witten invariants for general symplectic manifolds''). As a DFG-Heisenberg Fellow, he went to the Universität Paris VI/ Universität Paris VII from 2000 to 2002. From there, he was called to a professorship at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mark Gross (mathematician)
Mark William Gross (born 30 November 1965) is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry. Early life and education Mark William Gross was born on 30 November 1965 in Ithaca, New York, to Leonard Gross and Grazyna Gross. From 1982, he studied at Cornell University, graduating with a bachelor's degree in 1984. He gained a PhD in 1990 from the University of California, Berkeley, for research supervised by Robin Hartshorne with a thesis on the surfaces in the four-dimensional Grassmannian. Career From 1990 to 1993 he was an assistant professor at the University of Michigan and spent the academic year 1992–1993 on leave as a postdoctoral researcher at the Mathematical Sciences Research Institute (MSRI) in Berkeley. He was at Cornell University in 1993–1997 an assistant professor and in 1997–2001 an associate professor and then at University of California, San Diego in 2001–2013 a full professor. He was a visiting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Maryna Viazovska
Maryna Sergiivna Viazovska (, ; born 2 December 1984) is a Ukrainian mathematician known for her work in sphere packing. She is a full professor and Chair of Number Theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ... at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne in Switzerland. She was awarded the Fields Medal in 2022. Education and career Viazovska was born in Kyiv, the oldest of three sisters. Her father was a chemist who worked at the Antonov aircraft factory and her mother was an engineer. She attended a specialized secondary school for high-achieving students in science and technology, Kyiv Natural Science Lyceum No. 145. An influential teacher there, Andrii Knyazyuk, had previously worked as a professional research mathematician be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Scott Sheffield
Scott Sheffield (born October 20, 1973) is a professor of mathematics at the Massachusetts Institute of Technology. His primary research field is theoretical probability. Research Much of Sheffield's work examines conformal invariant objects which arise in the study of two-dimensional statistical physics models. He studies the Schramm–Loewner evolution SLE(κ) and its relations to a variety of other random objects. For example, he proved that SLE describes the interface between two Liouville quantum gravity surfaces that have been conformally welded together. In joint work with Oded Schramm, he showed that contour lines of the Gaussian free field are related to SLE(4). With Jason Miller, he developed the theory of Gaussian free field flow lines, which include SLE(κ) for all values of κ, as well as many variants of SLE. Sheffield and Bertrand Duplantier proved the Knizhnik–Polyakov–Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
