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Akshay Venkatesh
Akshay Venkatesh (born 21 November 1981) is an Australian mathematician and a professor (since 15 August 2018) at the School of Mathematics at the Institute for Advanced Study. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces, ergodic theory, and algebraic topology. He is the only Australian to have won medals at both the International Physics Olympiad and International Mathematical Olympiad, which he did at the age of 12. In 2018, he was awarded the Fields Medal for his synthesis of analytic number theory, Ergodic theory, homogeneous dynamics, topology, and representation theory. He is the second Australian and the second person of Indian descent to win the Fields Medal. He was on the Mathematical Sciences jury for the Infosys Prize in 2020. Early years Akshay Venkatesh was born in Delhi, India, and his family emigrated to Perth, Western Aus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Delhi
New Delhi (, , ''Naī Dillī'') is the Capital city, capital of India and a part of the NCT Delhi, National Capital Territory of Delhi (NCT). New Delhi is the seat of all three branches of the government of India, hosting the Rashtrapati Bhavan, Parliament House (India), Parliament House, and the Supreme Court of India. New Delhi is a Municipal governance in India, municipality within the NCT, administered by the New Delhi Municipal Council, NDMC, which covers mostly Lutyens' Delhi and a few adjacent areas. The municipal area is part of a larger List of districts in India, administrative district, the New Delhi district. Although colloquially ''Delhi'' and ''New Delhi'' are used interchangeably to refer to the National Capital Territory of Delhi, both are distinct entities, with both the municipality and the New Delhi district forming a relatively small part of the megacity of Delhi. The National Capital Region (India), National Capital Region is a much larger entity compri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perth, Western Australia
Perth is the capital and largest city of the Australian state of Western Australia. It is the fourth most populous city in Australia and Oceania, with a population of 2.1 million (80% of the state) living in Greater Perth in 2020. Perth is part of the South West Land Division of Western Australia, with most of the metropolitan area on the Swan Coastal Plain between the Indian Ocean and the Darling Scarp. The city has expanded outward from the original British settlements on the Swan River, upon which the city's central business district and port of Fremantle are situated. Perth is located on the traditional lands of the Whadjuk Noongar people, where Aboriginal Australians have lived for at least 45,000 years. Captain James Stirling founded Perth in 1829 as the administrative centre of the Swan River Colony. It was named after the city of Perth in Scotland, due to the influence of Stirling's patron Sir George Murray, who had connections with the area. It gained cit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delhi
Delhi, officially the National Capital Territory (NCT) of Delhi, is a city and a union territory of India containing New Delhi, the capital of India. Straddling the Yamuna river, primarily its western or right bank, Delhi shares borders with the state of Uttar Pradesh in the east and with the state of Haryana in the remaining directions. The NCT covers an area of . According to the 2011 census, Delhi's city proper population was over 11 million, while the NCT's population was about 16.8 million. Delhi's urban agglomeration, which includes the satellite cities of Ghaziabad, Faridabad, Gurgaon and Noida in an area known as the National Capital Region (India), National Capital Region (NCR), has an estimated population of over 28 million, making it the List of metropolitan areas in India, largest metropolitan area in India and the List of urban areas by population, second-largest in the world (after Tokyo). The topography of the medieval fort Purana Qila on the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India TV
India TV is a Hindi news channel based in Noida, Uttar Pradesh, India. The channel was launched on 20 May 2004 by Rajat Sharma and wife Ritu Dhawan. The channel is a subsidiary of Independent News Service, which was co-founded by Sharma and Dhawan in 1997. A rebranding of the channel took place in February 2022. History In 1997, Rajat Sharma and Ritu Dhawan set up Independent News Service (INS), the parent company which owns India TV. He co-founded India TV with his wife in April, 2004 from a studio in Film City, Noida, India TV. Its Broadcast Centre is in Sector 85, Noida, UP, India Prior to launching India TV, Rajat Sharma was a previously the anchor of '' Aap Ki Adalat'' on Zee News Zee News is an Indian Hindi-language news channel owned by Subhash Chandra's Essel Group. It launched on 27 August 1999 and is the flagship channel of the Zee Media Corporation. The channel has been involved in several controversies and ... and ''Janata Ki Adalat'' on Star News. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
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; connectedne ... [...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 ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. * Additive n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Australian Mathematics Trust
The Australian Mathematics Competition is a mathematics competition run by the Australian Maths Trust for students from year 3 up to year 12 in Australia, and their equivalent grades in other countries. Since its inception in 1976 in the Australian Capital Territory, the participation numbers have increased to around 600,000, with around 100,000 being from outside Australia, making it the world's largest mathematics competition. History The fore-runner of the competition, first held in 1976, was open to students within the Australian Capital Territory, and attracted 1200 entries. In 1976 and 1977 the outstanding entrants were awarded the Burroughs medal.Canberra Mathematical Association et al.: High school mathematics competition for the Burroughs medal : solutions and statistics, Canberra College of Advanced Education, 1976 In 1978, the competition became a nationwide event, and became known as the Australian Mathematics Competition for the Wales awards with 60,000 students from A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries, representing over 90% of the world's population, send teams of up to six students, plus one team leader, one deputy leader, and observers. The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions req ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Physics Olympiad
The International Physics Olympiad (IPhO) is an annual physics competition for high school students. It is one of the International Science Olympiads. The first IPhO was held in Warsaw, Poland in 1967. Each national delegation is made up of at most five student competitors plus two leaders, selected on a national level. Observers may also accompany a national team. The students compete as individuals, and must sit for intensive theoretical and laboratory examinations. For their efforts the students can be awarded gold, silver, or bronze medals or an honourable mention. The theoretical examination lasts 5 hours and consists of three questions. Usually these questions involve more than one part. The practical examination may consist of one laboratory examination of five hours, or two, which together take up the full five hours. History The idea of creating the International Physics Olympiad was conceived in Eastern Bloc countries, inspired by the 1959 established Internat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clay Mathematics Institute
The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's scientific activities are managed from the President's office in Oxford, United Kingdom. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the sponsorship of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI. While the institute is best known for its Millennium Prize Problems, it carries out a wide range of activities, including a postdoctoral program (ten Clay Research Fellows are supported currently), conferences, workshops, and summer schools. Governance The institute is run according to a standard structure comprising a scientific advisory committee that decides on grant-awarding and research proposals, and a board of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
