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Julian Sahasrabudhe
Julian Sahasrabudhe (born May 8, 1988) is a Canadian mathematician who is an assistant professor of mathematics at the University of Cambridge, in their Department of Pure Mathematics and Mathematical Statistics. His research interests are in extremal and probabilistic combinatorics, Ramsey theory, random polynomials and matrices, and combinatorial number theory. Life and education Sahasrabudhe grew up on Bowen Island, British Columbia, Canada. He studied music at Capilano College and later moved to study at Simon Fraser University where he completed his undergraduate degree in mathematics. After graduating in 2012, Julian received his Ph.D. in 2017 under the supervision of Béla Bollobás at the University of Memphis. Following his Ph.D., Sahasrabudhe was a Junior Research Fellow at Peterhouse, Cambridge from 2017 to 2021. He currently holds a position as an assistant professor in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Fraser University
Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located from downtown Vancouver, was established in 1965 and comprises more than 30,000 students and 160,000 alumni. The university was created in an effort to expand higher education across Canada. SFU is a member of multiple national and international higher education associations, including the Association of Commonwealth Universities, International Association of Universities, and Universities Canada. SFU has also partnered with other universities and agencies to operate joint research facilities such as the TRIUMF, Canada's national laboratory for particle and nuclear physics, which houses the world's largest cyclotron, and Bamfield Marine Station, a major centre for teaching and research in marine biology. Undergraduate and graduate programs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Morris (mathematician)
Robert (Rob) Morris is a mathematician who works in combinatorics, probability, graph theory and Ramsey theory. He is a researcher at IMPA. In 2015, Morris was awarded the European Prize in Combinatorics for "his profound results in extremal and probabilistic combinatorics particularly for his result on independent sets in hypergraphs which found immediately several applications in additive number theory and combinatorics, such as the solution of old problem of Erdős and for establishing tight bounds for Ramsey numbers, and also on random cellular automata and bootstrap problems in percolation." In 2016, he was one of the winners of the George Pólya Prize. He graduated with a Ph.D. from The University of Memphis in 2006 under the supervision of Béla Bollobás. He was awarded the 2018 Fulkerson Prize. Also in 2018, he was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro Rio de Janeiro ( , , ; literally 'River of January'), or simply Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Combinatorics
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive combinatorics is the special case when only the operations of addition and subtraction are involved. Ben Green explains arithmetic combinatorics in his review of "Additive Combinatorics" by Tao and Vu. Important results Szemerédi's theorem Szemerédi's theorem is a result in arithmetic combinatorics concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured. that every set of integers ''A'' with positive natural density contains a ''k'' term arithmetic progression for every ''k''. This conjecture, which became Szemerédi's theorem, generalizes the statement of van der Waerden's theorem. Green–Tao theorem and extensions The Gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are Multiple (mathematics), integer multiples of one another, as are the frequencies of the Harmonic series (music), harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Prize In Combinatorics
The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarded at Eurocomb 2003 in Prague. Recipients must not be older than 35. The most recent prize was awarded at Eurocomb 2021 in Barcelona (Online). * 2003 Daniela Kühn, Deryk Osthus, Alain Plagne. * 2005 Dmitry Feichtner-Kozlov * 2007 Gilles Schaeffer. * 2009 Peter Keevash, Balázs Szegedy * 2011 David Conlon, Daniel Kráľ * 2013 Wojciech Samotij, Tom Sanders * 2015 Karim Adiprasito, Zdeněk Dvořák, Rob Morris * 2017 Christian Reiher, Maryna Viazovska * 2019 Richard Montgomery and Alexey Pokrovskiy * 2021 Péter Pál Pach, Julian Sahasrabudhe, Lisa Sauermann, István Tomon See also * List of mathematics awards This list of mathematics awards is an index to articles about notable awards for mathematics. The list is organized b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Pomerance
Carl Bernard Pomerance (born 1944 in Joplin, Missouri) is an American number theorist. He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. He joined the faculty at the University of Georgia, becoming full professor in 1982. He subsequently worked at Lucent Technologies for a number of years, and then became a distinguished Professor at Dartmouth College. Contributions He has over 120 publications, including co-authorship with Richard Crandall of ''Prime numbers: a computational perspective'' (Springer-Verlag, first edition 2001, second edition 2005), and with Paul Erdős. He is the inventor of one of the integer factorization methods, the quadratic sieve algorithm, which was used in 1994 for the factorization of RSA-129. He is also one of the discoverers of the Adleman–Pomerance–Rumely primality test. Awards and honors He has won ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Konyagin
Sergei Vladimirovich Konyagin (russian: Серге́й Владимирович Конягин; born 25 April 1957) is a Russian mathematician. He is a professor of mathematics at the Moscow State University. Konyagin participated in the International Mathematical Olympiad for the Soviet Union, winning two consecutive gold medals with perfect scores in 1972 and 1973. At the age of 15, he became one of the youngest people to achieve a perfect score at the IMO. In 1990 Konyagin was awarded the Salem Prize. In 2012 he became a fellow of the American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, .... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kevin Ford (mathematician)
Kevin B. Ford (born 22 December 1967) is an American mathematician working in analytic number theory. Education and career He has been a professor in the department of mathematics of the University of Illinois at Urbana-Champaign since 2001. Prior to this appointment, he was a faculty member at the University of South Carolina. Ford received a Bachelor of Science in Computer Science and Mathematics in 1990 from the California State University, Chico. He then attended the University of Illinois at Urbana-Champaign, where he completed his doctoral studies in 1994 under the supervision of Heini Halberstam. Research Ford's early work focused on the distribution of Euler's totient function. In 1998, he published a paper that studied in detail the range of this function and established that Carmichael's totient function conjecture is true for all integers up to 10^. In 1999, he settled Sierpinski’s conjecture. In August 2014, Kevin Ford, in collaboration with Green, Konyagin a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covering System
In mathematics, a covering system (also called a complete residue system) is a collection :\ of finitely many residue classes a_i(\mathrm\ ) = \ whose union contains every integer. Examples and definitions The notion of covering system was introduced by Paul Erdős in the early 1930s. The following are examples of covering systems: # \, # \, # \. A covering system is called ''disjoint'' (or ''exact'') if no two members overlap. A covering system is called ''distinct'' (or ''incongruent'') if all the moduli n_i are different (and bigger than 1). Hough and Nielsen (2019) proved that any distinct covering system has a modulus that is divisible by either 2 or 3. A covering system is called ''irredundant'' (or ''minimal'') if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set) :\ of finitely many residue classes is called an m-cover if it covers every integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invertible Matrix
In linear algebra, an -by- square matrix is called invertible (also nonsingular or nondegenerate), if there exists an -by- square matrix such that :\mathbf = \mathbf = \mathbf_n \ where denotes the -by- identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix is uniquely determined by , and is called the (multiplicative) ''inverse'' of , denoted by . Matrix inversion is the process of finding the matrix that satisfies the prior equation for a given invertible matrix . A square matrix that is ''not'' invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is zero. Singular matrices are rare in the sense that if a square matrix's entries are randomly selected from any finite region on the number line or complex plane, the probability that the matrix is singular is 0, that is, it will "almost never" be singular. Non-square matrices (-by- matrices for which ) do not hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice. Applications Physics In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the spacings between the eigenvalues of a random matrix, and should depend only on the symmetry class of the underlying evolution. In solid-state physics, random matrices model the behaviour of large disordered Hamiltonians in the mean-field approximation. In quantum chaos, the Bohigas–Giannoni–Schmit (BGS) conjecture asserts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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