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Vijay Patodi
Vijay Kumar Patodi (12 March 1945 – 21 December 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the index theorem for elliptic operators. He was a professor at Tata Institute of Fundamental Research, Mumbai (Bombay). Education Patodi was a graduate of Government High School, Guna, Madhya Pradesh. He received his bachelor's degree from Vikram University, Ujjain, his master's degree from the Benaras Hindu University, and his Ph.D. from the University of Bombay under the guidance of M. S. Narasimhan and S. Ramanan at the Tata Institute of Fundamental Research. In the two papers based on his Ph.D. thesis, "Curvature and Eigenforms of the Laplace Operator" (''Journal of Differential Geometry''), and "An Analytical Proof of the Riemann-Roch-Hirzebruch Formula for Kaehler Manifolds" (also ''Journal of Differential Geometry''), Patodi made his f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guna, India
Guna is a city and a municipality in Guna district in the Indian state of Madhya Pradesh. It is the administrative headquarters of Guna District and is located on the banks of Parbati river. Geography Guna is located at . It has an average elevation of 474 metres (1555 ft). Climate Demographics As of 2011 Indian Census, Guna had a total population of 180,935, of which 94,464 were males and 86,471 were females. Population within the age group of 0 to 6 years was 24,447. The total number of literates in Guna was 125,295, which constituted 69.2% of the population with male literacy of 75.3% and female literacy of 62.6%. The effective literacy rate of 7+ population of Guna was 80.1%, of which male literacy rate was 87.2% and female literacy rate was 72.3%. The Scheduled Castes and Scheduled Tribes population was 27,631 and 3,623 respectively. Guna had 34383 households in 2011. India census A census is the procedure of systematically acquiring, recording an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mumbai (Bombay)
Mumbai (, ; also known as Bombay — List of renamed Indian cities and states#Maharashtra, the official name until 1995) is the capital city of the Indian States and union territories of India, state of Maharashtra and the ''de facto'' financial centre of India. According to the United Nations, as of 2018, Mumbai is the List of cities in India by population, second-most populous city in India after Delhi and the List of largest cities, eighth-most populous city in the world with a population of roughly 20 million (2 crore). As per the Indian government population census of 2011, Mumbai was the list of cities in India by population, most populous city in India with an estimated city proper population of 12.5 million (1.25 crore) living under the Municipal Corporation of Greater Mumbai, Brihanmumbai Municipal Corporation. Mumbai is the centre of the Mumbai Metropolitan Region, the sixth most populous metropolitan area in the world with a population of over 23 million ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vikram University Alumni , legendary king of India
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{{disambiguation ...
Vikram may refer to: * Vikram (name), a male name in the Hindu community * ''Vikram'' (1986 Tamil film) * ''Vikram'' (1986 Telugu film) * ''Vikram'' (2022 Tamil film) * Vikram (actor) (born 1966), Indian actor * Vikram (spacecraft), an Indian Moon lander * Vikram, a character in ''Baital Pachisi'' See also * Vikram Samvat (Vikram's Era, "V.S." or "B.S."), a calendar in India and the official calendar of Nepal * Vikramaditya Vikramaditya (IAST: ') was a legendary king who has been featured in hundreds of traditional stories including those in ''Baital Pachisi'' and ''Singhasan Battisi''. Many describe him as ruler with his capital at Ujjain (Pataliputra or Pratis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study Visiting Scholars
An institute is an organisational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or can also be a professional body. In some countries, institutes can be part of a university or other institutions of higher education, either as a group of departments or an autonomous educational institution without a traditional university status such as a "university institute" (see Institute of Technology). In some countries, such as South Korea and India, private schools are sometimes referred to as institutes, and in Spain, secondary schools are referred to as institutes. Historically, in some countries institutes were educational units imparting vocational training and often incorporating libraries, also known as mechanics' institutes. The word "institute" comes from a Latin word ''institutum'' meaning "facility" or "habit"; from ''instituere'' meaning "build", "create", "raise" or "educate". ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tata Institute Of Fundamental Research Alumni
Tata or TATA may refer to: Places * Jamshedpur, a city in Jharkhand, India also known as Tatanagar or Tata * Tata, Hungary, a town in Hungary * Tata Islands, a pair of small islands off the coast of New Zealand * Tata, Morocco, a city in Tata Province * Tata Province, Morocco * Țâța River, a tributary of the Ialomiţa River in Romania Companies * Tata Sons, India's largest conglomerate and owner of Tata Group * Tata Group, an Indian multinational conglomerate company ** List of entities associated with Tata Group People Surname * Tata family, an influential family of India owning the Tata Group ** Jamsetji Tata (1839–1904), known as the father of Indian industry ** Dorabji Tata (1859–1932), Indian industrialist and philanthropist ** Ratanji Tata (1871–1918), financier and philanthropist, son of Jamsetji Tata ** J. R. D. Tata (1904–1993), Indian pioneer aviator and founder of Tata Airlines ** Naval H. Tata (1904–1989), industrialist, recipient of Padma Bhu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Topologists
Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asian ethnic groups, referring to people of the Indian subcontinent, as well as the greater South Asia region prior to the 1947 partition of India * Anglo-Indians, people with mixed Indian and British ancestry, or people of British descent born or living in the Indian subcontinent * East Indians, a Christian community in India Europe * British Indians, British people of Indian origin The Americas * Indo-Canadians, Canadian people of Indian origin * Indian Americans, American people of Indian origin * Indigenous peoples of the Americas, the pre-Columbian inhabitants of the Americas and their descendants ** Plains Indians, the common name for the Native Americans who lived on the Great Plains of North America ** Native Americans in the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometers
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
η-invariant
In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues minus the number of negative eigenvalues. In practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by who used it to extend the Hirzebruch signature theorem to manifolds with boundary. The name comes from the fact that it is a generalization of the Dirichlet eta function. They also later used the eta invariant of a self-adjoint operator to define the eta invariant of a compact odd-dimensional smooth manifold. defined the signature defect of the boundary of a manifold as the eta invariant, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at ''s''=0 or 1 of a Shimizu L-function. Definition The eta invariant of self-adjoint operator ''A'' is given by ''η''''A''(0), where ''η'' is the analyti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raoul Bott
Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem. Early life Bott was born in Budapest, Hungary, the son of Margit Kovács and Rudolph Bott. His father was of Austrian descent, and his mother was of Hungarian Jewish descent; Bott was raised a Catholic by his mother and stepfather. Bott grew up in Czechoslovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II. Career Bott later went to college at McGill University in Montreal, where he studied electrical engineering. He then earned a PhD in mathematics from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled ''Electrical Network Theory'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isadore Singer
Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley. Singer is noted for his work with Michael Atiyah, proving the Atiyah–Singer index theorem in 1962, which paved the way for new interactions between pure mathematics and theoretical physics. In early 1980s, while a professor at Berkeley, Singer co-founded the Mathematical Sciences Research Institute (MSRI) with Shiing-Shen Chern and Calvin Moore. Biography Early life and education Singer was born on May 3, 1924, in Detroit, Michigan, to Polish Jewish immigrants. His father Simon was employed as a printer and only spoke Yiddish, and his mother, Freda (Rosemaity), worked as a seamstress. Singer learned English swiftly and subsequently taught it to the rest of his family. Isadore was born with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Life Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at the University of Oxford and the University of Cambridge and in the United States at the Institute for Advanced Study. He was the President of the Royal Society (1990–1995), founding director of the Isaac Newton Institute (1990–1996), master of Trinity College, Cambridge (1990–1997), chancellor of the University of Leicester (1995–2005), and the President of the Royal Society of Edinburgh (2005–2008). From 1997 until his death, he was an honorary professor in the University of Edinburgh. Atiyah's mathematical collaborators included Raoul Bott, Friedrich Hirzebruch and Isadore Sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
