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{{short description|Indian probabilist (born 1936)}}
{{Use Indian English|date=May 2015}}
{{Use dmy dates|date=May 2015}}
{{Infobox scientist
|name = K. R. Parthasarathy
|image = K. R. Parthasarathy.jpg
|image_size =
|caption =
|birth_date = {{Birth date and age|df=yes|1936|06|25}}<ref>[http://www.mathunion.org/Publications/Bulletins/38/IMU.EC/ParthasarathyKR.html Kalyanapuram Rangachari PARTHASARATY] {{Webarchive|url=https://web.archive.org/web/20140908135109/http://www.mathunion.org/Publications/Bulletins/38/IMU.EC/ParthasarathyKR.html |date=8 September 2014 }} at mathunion.org</ref>
|birth_place = [[Chennai|Madras]], India
|death_date =
|death_place =
|field = [[Mathematics]]
|work_institutions = [[Indian Statistical Institute]]
|alma_mater = [[Ramakrishna Mission Vivekananda College]], [[Indian Statistical Institute]]
|doctoral_advisor = [[C. R. Rao]]
|doctoral_students =
|known_for = [[Quantum stochastic calculus]]
|author_abbrev_bot =
|author_abbrev_zoo =
|influences =
|influenced =
|prizes = [[Shanti Swarup Bhatnagar Award]]<br />[[TWAS Prize]]
|footnotes =
|signature =
}}

'''Kalyanapuram Rangachari Parthasarathy''' (born 25 June 1936) is professor emeritus at the [[Indian Statistical Institute]] and a pioneer of [[quantum stochastic calculus]].

==Biography==
He was born in 1936 <ref name="Seventy-fifth birthday">{{cite web|last=[[Kalyan Bidhan Sinha]] and [[B. V. Rajarama Bhat]]|title=Professor K. R. Parthasarathy|url=https://www.math.lsu.edu/cosa/6-1-00%5Bpartha%5D.pdf|publisher=[[Louisiana State University]]}}</ref><ref name="Conferring on D.Sc degree">{{cite web|title=Conferring on him the degree of Doctor of Sciences|url=http://www.cmi.ac.in/events/honoris-causa/parthasarathy|publisher=[[Chennai Mathematical Institute]]}}</ref> at [[Chennai]]. He studied at the [[Ramakrishna Mission Vivekananda College]], where he completed the B.A. (Honours)
course in [[Mathematics]], and moved to the [[Indian Statistical Institute]], [[Kolkata]], where he completed his Ph.D., under the supervision of [[C. R. Rao]] in 1962. He was one of the "famous four"<ref name="Veeravalli S. Varadarajan">{{cite web|last=[[Kalyan Bidhan Sinha]] and [[B. V. Rajarama Bhat]]|title=Veeravalli S. Varadarajan|url=https://www.math.lsu.edu/cosa/6-1-00%5Bpartha%5D.pdf|publisher=[[Louisiana State University]]}}</ref> (the others were [[R. Ranga Rao]], [[Veeravalli S. Varadarajan]], and [[S. R. Srinivasa Varadhan]] ) in [[Indian Statistical Institute|ISI]] during 1956–1963. He was awarded the first Ph.D. degree of ISI.<ref name="Seventy-fifth birthday" /> He received the [[Shanti Swarup Bhatnagar Prize]] for Science and Technology in Mathematical Science in 1977 and the [[TWAS Prize]] in 1996.<ref name="Prizes and Awards">{{Cite web |url=http://twas.org/opportunities/prizes-and-awards |title=Prizes and Awards |date=2016 |publisher=The World Academy of Sciences}}</ref>

==Research==
He worked at the [[Steklov Mathematical Institute]], [[USSR Academy of Sciences]] (1962–63), as Lecturer where he collaborated with [[Andrey Kolmogorov]].<ref>{{cite web|title=Professor KR Parthasarathy|url=http://insaindia.org/detail.php?id=n76-0553|publisher=[[Indian National Science Academy]]|access-date=18 May 2013|archive-url=https://web.archive.org/web/20150901144928/http://insaindia.org/detail.php?id=n76-0553|archive-date=1 September 2015|url-status=dead}}</ref> Later he came in United Kingdom as Professor of Statistics in [[University of Sheffield]] (1964–68), [[University of Manchester]] (1968-70) and later at [[University of Nottingham]] where he collaborated with [[Robin Lyth Hudson]] on their pioneering work in quantum stochastic calculus.<ref name="Conferring on D.Sc degree" /><ref>{{cite web|last=D Applebaum|title=Robin Hudson's Pathless Path to Quantum Stochastic Calculus|url=https://www.applebaum.staff.shef.ac.uk/Hudpath.pdf|url-status=dead|archive-url=https://web.archive.org/web/20160304061146/https://www.applebaum.staff.shef.ac.uk/Hudpath.pdf|archive-date=4 March 2016|df=dmy-all}}</ref><ref>{{cite book|author1=Jinqiao Duan |author2=Shunlong Luo |author3=Caishi Wang |title=Recent development in stochastic dynamics and stochastic analysis|year=2010|publisher=World Scientific|isbn=9814277266|page=preface-x}}</ref><ref>{{cite web|last=K. R. Parthasarathy|title=Quantum Stochastic Calculus|url=https://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps|access-date=27 April 2013|archive-url=https://web.archive.org/web/20120728070024/http://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps|archive-date=28 July 2012|url-status=dead}}</ref> Then he returned to India, and after a few years in [[Bombay University]] and the [[Indian Institute of Technology, Delhi]], he came back in 1976 to the new [[Indian Statistical Institute, Delhi Centre]] and he stayed there until he retired in 1996.<ref name="Seventy-fifth birthday" />

He is the namesake of [[Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants]] along with [[Bertram Kostant]], [[R. Ranga Rao]] and [[Veeravalli S. Varadarajan]] which they introduced in 1967.<ref>K. R. Parthasarathy, R. Ranga Rao, and [[Veeravalli S. Varadarajan]]. "Representations of complex semi-simple Lie groups and Lie algebras." The Annals of Mathematics 85.3 (1967): 383-429</ref>

==Books authored==
Among the books he has authored are:
* K. R. Parthasarathy. [[Probability measure]]s on [[metric spaces]]. Vol. 352. [[American Mathematical Society]], 1967.
* [[Robin Lyth Hudson]] and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions." [[Communications in Mathematical Physics]] 93.3 (1984): 301–323.
* K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992.
* K. R. Parthasarathy and [[Klaus Schmidt (mathematician)|Klaus Schmidt]]. "[[Positive definite kernel]]s, continuous tensor products, and [[central limit theorem]]s of [[probability theory]]" (series: [[Lecture Notes in Mathematics]]). (1972).

==References==
{{Reflist}}

==External links==
*{{MathGenealogy|id=48989|title=Kalyanapuram Rangachari Parthasarathy}}
*[https://web.archive.org/web/20081004192714/http://www.isid.ac.in/~statmath/smfaculty/faculty.html K. R. Parthasaraty at Indian Statistical Institute (Delhi Center)]
*https://web.archive.org/web/20120728070024/http://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps

{{SSBPST recipients in Mathematical Science}}
{{Shanti Swarup Bhatnagar Laureates of Tamil Nadu}}

{{Authority control}}

{{DEFAULTSORT:Parthasarathy, K. R.}}
[[Category:1936 births]]
[[Category:Living people]]
[[Category:Indian statisticians]]
[[Category:20th-century Indian mathematicians]]
[[Category:21st-century Indian mathematicians]]
[[Category:Probability theorists]]
[[Category:Indian Statistical Institute alumni]]
[[Category:Indian Statistical Institute faculty]]
[[Category:Scientists from Chennai]]
[[Category:TWAS laureates]]
[[Category:Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science]]

K. R. Parthasarathy (probabilist) - Revision history

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