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Rajagopalan Parthasarathy
Rajagopalan Parthasarathy is an Indian mathematician who specialised in representation theory of Lie groups and algebras. He was awarded in 1985 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. Prof. Parthasarathy is an expert in representation theory of semisimple Lie groups. His initial work was on the realization of the so-called discrete series of representations of a semisimple Lie group in the space of Dirac Spinors. He made considerable progress in many central problems in representation theory. His work on the resolution of the Blattner's conjecture In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mode ... and the question of unitarisability of certain highest weight modules are significa ... [...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 operation i ... [...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] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1945 Births
1945 marked the end of World War II and the fall of Nazi Germany and the Empire of Japan. It is also the only year in which Nuclear weapon, nuclear weapons Atomic bombings of Hiroshima and Nagasaki, have been used in combat. Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: ** Nazi Germany, Germany begins Operation Bodenplatte, an attempt by the ''Luftwaffe'' to cripple Allies of World War II, Allied air forces in the Low Countries. ** Chenogne massacre: German prisoners are allegedly killed by American forces near the village of Chenogne, Belgium. * January 6 – WWII: A German offensive recaptures Esztergom, Kingdom of Hungary (1920–1946), Hungary from the Russians. * January 12 – WWII: The Soviet Union begins the Vistula–Oder Offensive in Eastern Europe, against the German Army (Wehrmacht), German Army. * January 13 – WWII: The Soviet Union begins the East Prussian Offensive, to eliminate German forces in East Pruss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Council Of Scientific & Industrial Research
The Council of Scientific and Industrial Research (IAST: ''vaigyanik tathā audyogik anusandhāna pariṣada''), abbreviated as CSIR, was established by the Government of India in September 1942 as an autonomous body that has emerged as the largest research and development organisation in India. CSIR is also among the world's largest publicly funded R&D organisation which is pioneering sustained contribution to S&T human resource development in the country. , it runs 37 laboratories/institutes, 39 outreach centres, 3 Innovation Centres and 5 units throughout the nation, with a collective staff of over 14,000, including a total of 4,600 scientists and 8,000 technical and support personnel. Although it is mainly funded by the Ministry of Science and Technology, it operates as an autonomous body through the Societies Registration Act, 1860. The research and development activities of CSIR include aerospace engineering, structural engineering, ocean sciences, life sciences and he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations average to between 73–55 ka.", "Modern human beings—''Homo sapiens''—originated in Africa. Then, int ... [...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 operation i ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blattner's Conjecture
In mathematics, Blattner's conjecture or Blattner's formula is a description of the discrete series representations of a general semisimple group ''G'' in terms of their restricted representations to a maximal compact subgroup ''K'' (their so-called ''K''-types). It is named after Robert James Blattner, despite not being formulated as a conjecture by him. Statement Blattner's formula says that if a discrete series representation with infinitesimal character λ is restricted to a maximal compact subgroup ''K'', then the representation of ''K'' with highest weight μ occurs with multiplicity :\sum_\epsilon(\omega)Q(w(\mu+\rho_c)-\lambda-\rho_n) where :''Q'' is the number of ways a vector can be written as a sum of non-compact positive roots :WK is the Weyl group of ''K'' :ρc is half the sum of the compact roots :ρn is half the sum of the non-compact roots :ε is the sign character of WK. Blattner's formula is what one gets by formally restricting the Harish-Chandra character formul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction). Combining these two ideas, one obtains a continuous group where multiplying points and their inverses are continuous. If the multiplication and taking of inverses are smooth (differentiable) as well, one obtains a Lie group. Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the rotational symmetry in three dimensions (given by the special orthogonal group \text(3)). Lie groups are widely used in many parts of modern mathematics and physics. Lie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bombay
The University of Mumbai is a collegiate, state-owned, public research university in Mumbai. The University of Mumbai is one of the largest universities in the world. , the university had 711 affiliated colleges. Ratan Tata is the appointed head of the advisory council. History In accordance with "Wood's despatch", drafted by Sir Charles Wood in 1854, the University of Bombay was established in 1857 after the presentation of a petition from the Bombay Association to the British colonial government in India. The University of Mumbai was modelled on similar universities in the United Kingdom, specifically the University of London. The first departments established were the Faculty of Arts at Elphinstone College in 1835 and the Faculty of Medicine at Grant Medical College in 1845. Both colleges existed before the university was founded and surrendered their degree-granting privileges to the university. The first degrees awarded in 1862 were Bachelor of Arts and Licentiate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
