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M. S. Narasimhan
Mudumbai Seshachalu Narasimhan (7 June 1932 – 15 May 2021) was an Indian mathematician. His focus areas included number theory, algebraic geometry, representation theory, and partial differential equations. He was a pioneer in the study of moduli spaces of holomorphic vector bundles on projective varieties. His work is considered the foundation for Kobayashi–Hitchin correspondence that links differential geometry and algebraic geometry of vector bundles over complex manifolds. He was also known for his collaboration with mathematician C. S. Seshadri, for their proof of the Narasimhan–Seshadri theorem which proved the necessary conditions for stable vector bundles on a Riemann surface. He was a recipient of the Padma Bhushan, India's third highest civilian honor, in 1990, and the Ordre national du Mérite from France in 1989. He was an elected Fellow of the Royal Society, London. He was also the recipient of Shanti Swarup Bhatnagar Prize in 1975 and was the only Indian to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tandarai
Tandarai is a Panchayat town in Tiruvanamalai district, Tamil Nadu India. It is the fourth largest town in Kilpennathur taluk and has one railway station. It lies between Vettavalam and Veraiyur and has a population of 5201 and altitude of 81m. Cities and towns in Tiruvannamalai district {{Tiruvannamalai-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moduli Space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Motivation Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shanti Swarup Bhatnagar Prize For Science And Technology
The Shanti Swarup Bhatnagar Prize for Science and Technology (SSB) is a science award in India given annually by the Council of Scientific and Industrial Research (CSIR) for notable and outstanding research, Applied science, applied or Fundamental science, fundamental, in biology, chemistry, environmental science, engineering, mathematics, medicine, and physics. The prize recognizes outstanding Indian work (according to the view of Council of Scientific and Industrial Research, CSIR awarding committee) in science and technology. It is the most coveted award in Interdisciplinarity, multidisciplinary science in India. The award is named after the founder Director of the Council of Scientific & Industrial Research, Shanti Swaroop Bhatnagar, Shanti Swarup Bhatnagar. It was first awarded in 1958. Any citizen of India engaged in research in any field of science and technology up to the age of 45 years is eligible for the prize. The prize is awarded on the basis of contributions made thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by King Charles II as The Royal Society and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the Society's President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordre National Du Mérite
The Ordre national du Mérite (; en, National Order of Merit) is a French order of merit with membership awarded by the President of the French Republic, founded on 3 December 1963 by President Charles de Gaulle. The reason for the order's establishment was twofold: to replace the large number of ministerial orders previously awarded by the ministries; and to create an award that can be awarded at a lower level than the Legion of Honour, which is generally reserved for French citizens. It comprises about 185,000 members; 306,000 members have been admitted or promoted in 50 years. History The Ordre national du Mérite comprises about 185,000 members; 306,000 members have been admitted or promoted in 50 years. Half of its recipients are required to be women. Defunct ministerial orders The Ordre national du Mérite replaced the following ministerial and colonial orders: Colonial orders * '' Ordre de l'Étoile d'Anjouan'' (1874) (Order of the Star of Anjouan) * ''Ordre du N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padma Bhushan
The Padma Bhushan is the third-highest civilian award in the Republic of India, preceded by the Bharat Ratna and the Padma Vibhushan and followed by the Padma Shri. Instituted on 2 January 1954, the award is given for "distinguished service of a high order...without distinction of race, occupation, position or sex." The award criteria include "service in any field including service rendered by Government servants" including doctors and scientists, but exclude those working with the public sector undertakings. , the award has been bestowed on 1270 individuals, including twenty-four posthumous and ninety-seven non-citizen recipients. The Padma Awards Committee is constituted every year by the Prime Minister of India and the recommendations for the award are submitted between 1 May and 15 September. The recommendations are received from all the state and the union territory governments, as well as from Ministries of the Government of India, Bharat Ratna and Padma Vibhushan a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Surface
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. The main interest in Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm. Every Riemann surface is a two-dimensional real analytic manifold (i.e., a surface), but it contains more structure (specifically a complex structure) which is needed for the unambiguous definitio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Vector Bundle
In mathematics, a stable vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may be built from stable ones using Harder–Narasimhan filtration. Stable bundles were defined by David Mumford in and later built upon by David Gieseker, Fedor Bogomolov, Thomas Bridgeland and many others. Motivation One of the motivations for analyzing stable vector bundles is their nice behavior in families. In fact, Moduli spaces of stable vector bundles can be constructed using the Quot scheme in many cases, whereas the stack of vector bundles \mathbfGL_n is an Artin stack whose underlying set is a single point. Here's an example of a family of vector bundles which degenerate poorly. If we tensor the Euler sequence of \mathbb^1 by \mathcal(1) there is an exact sequence0 \to \mathcal(-1) \to \mathcal\oplus \mathcal \to \mathcal(1) \to 0which represents a non-zero element in v \in \text^1(\mathcal(1),\m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Narasimhan–Seshadri Theorem
In mathematics, the Narasimhan–Seshadri theorem, proved by , says that a holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible projective unitary representation of the fundamental group. The main case to understand is that of topologically trivial bundles, i.e. those of degree zero (and the other cases are a minor technical extension of this case). This case of the Narasimhan–Seshadri theorem says that a degree zero holomorphic vector bundle over a Riemann surface is stable if and only if it comes from an irreducible unitary representation of the fundamental group of the Riemann surface. gave another proof using differential geometry, and showed that the stable vector bundles have an essentially unique unitary connection of constant (scalar) curvature. In the degree zero case, Donaldson's version of the theorem says that a degree zero holomorphic vector bundle over a Riemann surface is stable if and only if it admits a flat unit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Manifold
In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in \mathbb^n, such that the transition maps are holomorphic. The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold. Implications of complex structure Since holomorphic functions are much more rigid than smooth functions, the theories of smooth and complex manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example, the Whitney embedding theorem tells us that every smooth ''n''-dimensional manifold can be embedded as a smooth submanifold of R2''n'', whereas it is "rare" for a complex manifold to have a holomorphic embedding into C''n''. Consider for example any compact connected complex manifold ''M'': any holomorphic function on it is cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X. The simplest example is the case that the family of vector spaces is constant, i.e., there is a fixed vector space V such that V(x)=V for all x in X: in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X\times V over X. Such vector bundles are said to be ''trivial''. A more complicated (and prototypical) class of examples are the tangent bundles of smooth (or differentiable) manifolds: to every point of such a manifold w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
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 structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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