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Shreeram Abhyankar
Shreeram Shankar Abhyankar (22 July 1930 – 2 November 2012) was an Indian American mathematician known for his contributions to algebraic geometry. At the time of his death, he held the Marshall Distinguished Professor of Mathematics Chair at Purdue University, and was also a professor of computer science and industrial engineering. He is known for Abhyankar's conjecture of finite group theory. His latest research was in the area of computational and algorithmic algebraic geometry. Career Abhyankar was born during the late British Raj 22 July in a MarathiChitpavan Brahmin family in Ujjain, Madhya Pradesh, India. He earned his B.Sc. from the Royal Institute of Science of University of Mumbai in 1951, his M.A. at Harvard University in 1952, and his Ph.D. at Harvard in 1955. His thesis, written under the direction of Oscar Zariski, was titled ''Local uniformization on algebraic surfaces over modular ground fields''. Before going to Purdue, he was an associate professor of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called Grothendieck's relative point of view, "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century. Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des Hautes Études Scientifiques, Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He receive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abhyankar's Conjecture
In abstract algebra, Abhyankar's conjecture for affine curves is a conjecture of Shreeram Abhyankar posed in 1957, on the Galois groups of algebraic function fields of characteristic ''p''. The soluble case was solved by Serre in 1990 and the full conjecture was proved in 1994 by work of Michel Raynaud and David Harbater.. Statement The problem involves a finite group ''G'', a prime number ''p'', and the function field ''K(C)'' of a nonsingular integral algebraic curve ''C'' defined over an algebraically closed field ''K'' of characteristic ''p''. The question addresses the existence of a Galois extension ''L'' of ''K''(''C''), with ''G'' as Galois group, and with specified ramification. From a geometric point of view, ''L'' corresponds to another curve ', together with a morphism :π : ' → ''C''. Geometrically, the assertion that π is ramified at a finite set ''S'' of points on ''C'' means that π restricted to the complement of ''S'' in ''C'' is an étale morphism. This i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chitpavan
The Chitpavan Brahmin or the Kokanastha Brahmin is a Hindu Maharashtrian Brahmin community inhabiting Konkan, the coastal region of the state of Maharashtra. Initially working as messengers and spies in the late seventeenth century, the community came into prominence during the 18th century when the heirs of Peshwa from the Bhat family of Balaji Vishwanath became the de facto rulers of the Maratha empire. Until the 18th century, the Chitpavans were held in low esteem by the Deshastha, the older established Brahmin community of Karnataka-Maharashtra region. As per Jayant Lele, the influence of the Chitpavans in the Peshwa era as well as the British era has been greatly exaggerated because even during the time of the most prominent Peshwas, their political legitimacy and their intentions were not trusted by all levels of the administration, not even by Shivaji's successors. He adds that after the defeat of Peshwas in the Anglo-Maratha wars, Chitpavans were one of the Hindu c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marathi People
The Marathi people (; Marathi language, Marathi: , ''Marāṭhī lōk'') or Marathis (Marathi: मराठी, ''Marāṭhī'') are an Indo-Aryan peoples, Indo-Aryan ethnolinguistic group who are native to Maharashtra in western India. They natively speak Marathi language, Marathi, an Indo-Aryan languages, Indo-Aryan language. Maharashtra was formed as a Marathi-speaking state of India on 1 May 1960, as part of a nationwide linguistic reorganisation of the States and union territories of India, Indian states. The term "Maratha" is generally used by historians to refer to all Marathi-speaking peoples, irrespective of their Caste system in India, caste; However, it may refer to a Maharashtrian caste known as the Maratha (caste), Maratha which also includes farmer sub castes like the Kunbis. The Marathi community came into political prominence in the 17th century, when the Maratha Empire was established by Shivaji in 1674. Etymology According to R. G. Bhandarkar, the term Mara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
British Raj
The British Raj ( ; from Hindustani language, Hindustani , 'reign', 'rule' or 'government') was the colonial rule of the British The Crown, Crown on the Indian subcontinent, * * lasting from 1858 to 1947. * * It is also called Crown rule in India, * * * * or direct rule in India. * Quote: "Mill, who was himself employed by the British East India company from the age of seventeen until the British government assumed direct rule over India in 1858." * * The region under British control was commonly called India in contemporaneous usage and included areas directly administered by the United Kingdom of Great Britain and Ireland, United Kingdom, which were collectively called ''Presidencies and provinces of British India, British India'', and areas ruled by indigenous rulers, but under British British paramountcy, paramountcy, called the princely states. The region was sometimes called the Indian Empire, though not officially. As ''India'', it was a founding member of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computation
A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. Computer science is an academic field that involves the study of computation. Introduction The notion that mathematical statements should be 'well-defined' had been argued by mathematicians since at least the 1600s, but agreement on a suitable definition proved elusive. A candidate definition was proposed independently by several mathematicians in the 1930s. The best-known variant was formalised by the mathematician Alan Turing, who defined a well-defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine. Other (mathematically equivalent) definitions include Alonzo Church's '' lambda-defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic variety, algebraic varieties, which are geometric manifestations of solution set, solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are line (geometry), lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscate of Bernoulli, lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular point of a curve, singular p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian American
Indian Americans are Americans whose ancestry originates wholly or partly from India. The terms Asian Indian and East Indian are used to avoid confusion with Native Americans in the United States, Native Americans in the United States, who are also referred to as "Indians" or "American Indians." With a population of more than 5.4 million, Indian Americans make up approximately 1.6% of the U.S. population and are the largest group of South Asian Americans, the largest Asian-alone group, and the second-largest group of Asian Americans after Chinese Americans. The Indian American population started increasing, especially after the 1980s, with U.S. migration policies that attracted highly skilled and educated Indian immigrants., quote="Educational exchange programs, new temporary visas for highly skilled workers, and expanded employment-based immigration channels opened pathways for highly skilled and educated Indian immigrants" Indian Americans have the highest List of ethnic gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
