Kalyanapuram Rangachari Parthasarathy (born 25 June 1936) is professor emeritus at the

Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta C ...

and a pioneer of

quantum stochastic calculus Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum ...

Biography

He was born in 1936 at

Chennai Chennai (, ), formerly known as Madras ( the official name until 1996), is the capital city of Tamil Nadu, the southernmost Indian state. The largest city of the state in area and population, Chennai is located on the Coromandel Coast of th ...

, into a modest but deeply religious

Hindu Hindus (; ) are people who religiously adhere to Hinduism.Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pages 35–37 Historically, the term has also been used as a geographical, cultural, and later religious identifier for ...

Brahmin Brahmin (; sa, ब्राह्मण, brāhmaṇa) is a varna as well as a caste within Hindu society. The Brahmins are designated as the priestly class as they serve as priests (purohit, pandit, or pujari) and religious teachers (guru ...

family. He studied at the

Ramakrishna Mission Vivekananda College Ramakrishna Mission Vivekananda College, named after Swami Vivekananda, was formally inaugurated on 21 June 1946 by professor, philosopher, and politician, Sarvepalli Radhakrishnan. It is in Mylapore, the centre of Chennai, India, on 20 acres (81 ...

, where he completed the B.A. (Honours) course 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 modern mathematics ...

, and moved to the

Kolkata Kolkata (, or , ; also known as Calcutta , the official name until 2001) is the capital of the Indian state of West Bengal, on the eastern bank of the Hooghly River west of the border with Bangladesh. It is the primary business, comme ...

, where he completed his Ph.D., under the supervision of

C. R. Rao Calyampudi Radhakrishna Rao FRS (born 10 September 1920), commonly known as C. R. Rao, is an Indian-American mathematician and statistician. He is currently professor emeritus at Pennsylvania State University and Research Professor at the Un ...

in 1962. He was one of the "famous four" (the others were R. Ranga Rao,

Veeravalli S. Varadarajan Veeravalli Seshadri Varadarajan (18 May 1937 – 25 April 2019) was an Indian mathematician at the University of California, Los Angeles, who worked in many areas of mathematics, including probability, Lie groups and their group representation ...

, and

S. R. Srinivasa Varadhan Sathamangalam Ranga Iyengar Srinivasa Varadhan FRS (born 2 January 1940) is an Indian American mathematician, widely recognised as one of the most influential mathematicians of the 20th century. He is known for his fundamental contributions to ...

) in ISI during 1956–1963. He was awarded the first Ph.D. degree of ISI. He received the

Shanti Swarup Bhatnagar Prize 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 Fundamenta ...

for Science and Technology in Mathematical Science in 1977 and the

TWAS Prize This is a list of recipients of the TWAS Prize, awarded annually by The World Academy of Sciences (TWAS). Summary Agricultural Sciences Biology Chemistry Earth Sciences Engineering Sciences Mathematics Medical Sc ...

in 1996.

Research

He worked at the

Steklov Mathematical Institute Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...

USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...

(1962–63), as Lecturer where he collaborated with

Andrey Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

. Later he came to United Kingdom as Professor of Statistics in

University of Sheffield , mottoeng = To discover the causes of things , established = – University of SheffieldPredecessor institutions: – Sheffield Medical School – Firth College – Sheffield Technical School – University College of Sheffield , type = Pu ...

(1964–68),

University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...

(1968–70) and later at

University of Nottingham The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...

where he collaborated with

Robin Lyth Hudson Robin Lyth Hudson was a British mathematician notable for his contribution to quantum probability. Education and career Robin Lyth Hudson received his Ph.D. from the University of Oxford in 1966 under John T. Lewis with a thesis entitled ''Gene ...

on their pioneering work in quantum stochastic calculus. Then he returned to India, and after a few years in

Bombay University 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 ...

and the

Indian Institute of Technology, Delhi The Indian Institute of Technology, Delhi is a public institute of technology located in New Delhi, India. It is one of the 23 IITs created to be Centres of Excellence for training, research and development in science, engineering and technolo ...

, he came back in 1976 to the new

Indian Statistical Institute, Delhi Centre Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...

and he stayed there until he retired in 1996. He is the namesake of Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

, R. Ranga Rao and

which they introduced in 1967.K. R. Parthasarathy, R. Ranga Rao, and

. "Representations of complex semi-simple Lie groups and Lie algebras." The Annals of Mathematics 85.3 (1967): 383-429

Books authored

Among the books he has authored are: * K. R. Parthasarathy.

Probability measure In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as ''countable additivity''. The difference between a probability measure and the more gener ...

s on

metric spaces In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...

. Vol. 352.

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 1967. *

and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions."

Communications in Mathematical Physics ''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, sta ...

93.3 (1984): 301–323. * K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992. * K. R. Parthasarathy and Klaus Schmidt. "

Positive definite kernel In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced by James Mercer (mathematician), James Mercer in the early 20th centur ...

s, continuous tensor products, and

central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselv ...

s of

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

" (series:

Lecture Notes in Mathematics ''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Spr ...

). (1972).

References

External links

*
K. R. Parthasaraty at Indian Statistical Institute (Delhi Center)
*https://web.archive.org/web/20120728070024/http://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps {{DEFAULTSORT:Parthasarathy, K. R. 1936 births Living people Indian statisticians 20th-century Indian mathematicians 21st-century Indian mathematicians Probability theorists Indian Statistical Institute alumni Academic staff of the Indian Statistical Institute Scientists from Chennai TWAS laureates Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science