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{{Short description|Indian mathematician}}
{{Use dmy dates|date=July 2018}}
{{Use Indian English|date=July 2018}}
{{Infobox scientist
| name = Veeravalli S. Varadarajan
| image = Varadarajan.jpg
| caption =
| birth_date = {{birth date|1937|5|18|df=y}}
| birth_place = [[Bangalore|Bengalaru]], India <ref name=long_innings />
| death_date = {{death date and age|2019|4|25|1937|5|18|df=y}}
| death_place = [[Santa Monica, California]], U.S.
| residence =
| citizenship =
| nationality = [[India]]n
| ethnicity =
| field = [[Mathematics]]
| work_institutions = [[University of California, Los Angeles]]<br>[[Indian Statistical Institute]], Kolkata
| alma_mater = [[Loyola College, Chennai|Loyola College, Madras]]<br>[[Presidency College, Chennai|Presidency College, Madras]]<br>[[Indian Statistical Institute]], Kolkata
| doctoral_advisor = [[C. R. Rao]]
| doctoral_students =
| known_for = [[Trombi–Varadarajan theorem]]
| author_abbrev_bot =
| author_abbrev_zoo =
| influences =
| influenced =
| prizes = [[Onsager Medal]]
| religion =
| footnotes =
| signature =
}}

'''Veeravalli Seshadri<ref>http://www.worldcat.org/identities/lccn-n50044956/</ref> Varadarajan''' (18 May 1937 – 25 April 2019)<ref>{{Cite web|url=http://id.loc.gov/authorities/names/n50044956.html|title = Varadarajan, V. S. - LC Linked Data Service: Authorities and Vocabularies | Library of Congress, from LC Linked Data Service: Authorities and Vocabularies (Library of Congress)}}</ref><ref>https://www.math.ucla.edu/news/memoriam-veeravalli-seshadri-varadarajan</ref><ref>https://www.ias.ac.in/public/Volumes/reso/024/09/0941-0946.pdf</ref> was an Indian mathematician at the [[University of California, Los Angeles]], who worked in many areas of mathematics, including probability, [[Lie group]]s and their [[group representation|representations]], quantum mechanics, differential equations, and supersymmetry.

==Biography==

Varadarajan's father, Seshadri, was an Inspector of Schools in the Department of Education. He was transferred to Madras where the medium of instruction was generally English. After Varadarajan completed his high school studies, he joined Intermediate for two years at [[Loyola College, Chennai|Loyola College, Madras]] where he was taught mathematics by K.A. Adivarahan, a very strict disciplinarian who made a strong impression on him.<ref name=long_innings>{{Cite web|url=http://bhavana.org.in/reflections-on-a-long-innings/|title=Reflections on a Long Innings – Bhāvanā|language=en-US|access-date=2019-07-30}}</ref><ref>{{Cite web|url=https://thewire.in/the-sciences/v-s-varadarajan-reflections-on-a-long-innings|title=V.S. Varadarajan: Reflections on a Long Innings|website=The Wire|access-date=2019-07-30}}</ref> Varadarajan received his undergraduate degree in 1957 from [[Presidency College, Chennai|Presidency College, Madras]] and his doctorate in 1960 from the [[Indian Statistical Institute]] in Calcutta, under the supervision of [[C. R. Rao]].<ref>{{Cite web|url=https://www.genealogy.math.ndsu.nodak.edu/id.php?id=36691|title=Veeravalli Varadarajan - the Mathematics Genealogy Project}}</ref> He was one of the "famous four"<ref name="Veeravalli S. Varadarajan">{{cite web|first1=Kalyan Bidhan | last1=Sinha | author-link1=Kalyan Bidhan Sinha | first2=B. V. Rajarama | last2=Bhat | author-link2=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> at the [[Indian Statistical Institute]] during 1956-1963 (the others being
[[R. Ranga Rao]], [[K. R. Parthasarathy (probabilist)|K. R. Parthasarathy]], and [[S. R. Srinivasa Varadhan]]). In 1960, after his doctorate, Varadarajan went to Princeton University as a post-doctoral fellow and in the Fall of 1960 he went to the University of Washington, Seattle where he spent the academic year, followed by a year at the Courant Institute at NYU, after which he returned to the Indian Statistical Institute in 1962.<ref>{{cite book |last1=Varadarajan |first1=V. S. |title=Reflections on Quanta, Symmetries, and Supersymmetries |year=2011 |url=https://archive.org/details/reflectionsonqua00vara |url-access=limited |publisher=Springer-Verlag |pages=[https://archive.org/details/reflectionsonqua00vara/page/n19 8]–10|isbn=9781441906663 }}</ref> He joined the Department of Mathematics at UCLA in 1965. Varadarajan was a member of the [[Institute for Advanced Study]] during the periods September 1968 until December 1968 and January 1976 until June 1976.<ref>{{Cite web|url=https://www.ias.edu/scholars/veeravalli-s-varadarajan|title = Veeravalli S. Varadarajan - Scholars | Institute for Advanced Study|date = 9 December 2019}}</ref> In March 2019, it was announced by UCLA that Varadarajan and his wife had donated $1 million to the Department of Mathematics at UCLA to establish the Ramanujan Visiting Professorship.<ref>{{Cite web|url=http://newsroom.ucla.edu/releases/professor-emeritus-gives-1-million-to-bring-visiting-mathematics-faculty-to-ucla|title=Professor emeritus gives $1 million to bring visiting mathematics faculty to UCLA}}</ref>

==Contributions==

Varadarajan's early work, including his doctoral thesis, was in the area of probability theory. He then moved into [[representation theory]] where he has done some of his best known work. He has also done work in mathematical physics, in particular quantum theory and p-adic themes in physics. In the 1980s, he wrote a series of papers with [[Donald Babbitt]] on the theory of differential equations with irregular singularities. His latest work has been in supersymmetry.

He introduced [[Kostant–Parthasarathy–Ranga Rao–Varadarajan determinant]]s along with [[Bertram Kostant]], [[K. R. Parthasarathy (probabilist)|K. R. Parthasarathy]] and [[R. Ranga Rao]] in 1967,<ref>{{cite journal | last1 = Parthasarathy | first1 = K. R. | author-link = K. R. Parthasarathy (probabilist) | last2 = Rao | first2 = R. Ranga | last3 = Varadarajan | first3 = V. S. | year = 1967 | title = Representations of complex semi-simple Lie groups and Lie algebras | journal = [[Annals of Mathematics]] | volume = 85 | issue = 3| pages = 383–429 | doi=10.2307/1970351| jstor = 1970351 | url = http://projecteuclid.org/euclid.bams/1183527963 }}</ref> the [[Trombi–Varadarajan theorem]]<ref>{{cite journal | last1 = Trombi | first1 = P. C. | last2 = Varadarajan | first2 = V. S. | year = 1972 | title = Asymptotic behaviour of eigen functions on a semisimple Lie group: The discrete spectrum | doi = 10.1007/bf02392217 | journal = [[Acta Mathematica]] | volume = 129 | issue = 1| pages = 237–280 | doi-access = free }}</ref> in 1972 and the [[Enright–Varadarajan module]]s<ref>{{cite journal | last1 = Enright | first1 = Thomas J. | last2 = Varadarajan | first2 = V. S. | year = 1975 | title = On an infinitesimal characterization of the discrete series | journal = [[Annals of Mathematics]] | volume = 102 | issue = 1| pages = 1–15 | doi=10.2307/1970970| jstor = 1970970 }}</ref> in 1975.

==Recognition==

He was awarded the [[Onsager Medal]] in 1998 for his work. He was recognized along with 23 Indian and Indian American members "who have made outstanding contributions to the creation, exposition advancement, communication, and utilization of mathematics" by the Fellows of the [[American Mathematical Society]] program in 1 November 2012.<ref>{{cite web|title=American Mathematical Society Honors 23 Indians |url=http://www.indiawest.com/news/8170-american-mathematical-society-honors-23-indians.html |work=Nov 1, 2012 |publisher=India-West |access-date=19 December 2012 |url-status=unfit |archive-url=https://web.archive.org/web/20121223063220/http://www.indiawest.com/news/8170-american-mathematical-society-honors-23-indians.html |archive-date=23 December 2012 }}</ref>

==Bibliography==
*Varadarajan, Veeravalli S (1984). Geometry of quantum theory, Springer-Verlag. 1st Edition 1968.
*{{Citation|last1=Varadarajan|first1=V. S.|title=Lie groups, Lie algebras, and their representations|url=https://books.google.com/books?id=3tGugV-HhtkC|publisher= [[Springer Verlag]]|isbn=978-0387909691|year=1984}}; {{cite book|title=1st edition|year=1974}}<ref>{{cite journal|author=Knapp, A. W.|author-link=Anthony W. Knapp|title=Review: ''Lie groups, Lie algebras, and their representations'', by V. S. Varadarajan; and ''Compact Lie groups and their representations'', by D. P. Želobenko|journal=Bull. Amer. Math. Soc. (N.S.)|year=1975|volume=81|issue=5|pages=865–872|doi=10.1090/s0002-9904-1975-13866-3|url=http://www.ams.org/journals/bull/1975-81-05/S0002-9904-1975-13866-3/S0002-9904-1975-13866-3.pdf|doi-access=free}}</ref>
*{{Citation|last1=Varadarajan|first1=V. S.|title=Harmonic analysis on real reductive groups|publisher=Springer-Verlag|year=1977}}<ref>{{cite journal|author=Herb, Rebecca A.|author-link=Rebecca A. Herb|title=Review: ''Harmonic analysis on real reductive groups'', by V. S. Varadarajan|journal=Bull. Amer. Math. Soc. (N.S.)|year=1979|volume=1|issue=2|pages=398–401|doi=10.1090/s0273-0979-1979-14614-7|url=http://www.ams.org/journals/bull/1979-01-02/S0273-0979-1979-14614-7/S0273-0979-1979-14614-7.pdf|doi-access=free}}</ref>
*{{Citation|last1=Gangolli|first1=Ramesh|last2=Varadarajan|first2=V. S.|title=Harmonic analysis of spherical functions on real reductive groups|publisher=Springer-Verlag|year=1983}}<ref>{{cite journal|author=Barbasch, D.|title=Review: ''Harmonic analysis of spherical functions on real reductive groups'', by R. Gangolli and V. S. Varadarajan|journal=[[Bulletin of the American Mathematical Society]] |series= (N.S.)| year=1990|volume=23|issue=2|pages=598–604|doi=10.1090/s0273-0979-1990-15996-8|url=http://www.ams.org/journals/bull/1990-23-02/S0273-0979-1990-15996-8/S0273-0979-1990-15996-8.pdf|doi-access=free}}</ref>
*{{Citation|last1=Varadarajan|first1=V. S.|title=An Introduction to Harmonic Analysis on Semisimple Lie Groups|url=https://books.google.com/books?id=seycdRenNfoC|publisher=[[Cambridge University Press]]| year=1999|isbn=9780521663625}}; {{cite book|title=1st edition|year=1989}}<ref>{{cite journal|last=Wolf|first= Joseph A.|author-link=Joseph A. Wolf|title=Review: ''An introduction to harmonic analysis on semisimple Lie groups'', by V. S. Varadarjan|journal=[[Bulletin of the American Mathematical Society]] |series= (N.S.)|year=1993|volume=28|issue=2|pages=367–370|doi=10.1090/s0273-0979-1993-00365-3|url=http://www.ams.org/journals/bull/1993-28-02/S0273-0979-1993-00365-3/S0273-0979-1993-00365-3.pdf|doi-access=free}}</ref>
*{{Citation |last1=Varadarajan |first1=V. S. |title=Algebra in Ancient and Modern Times |date=1998 |publisher=AMS & Hindustan Book Agency |url=https://bookstore.ams.org/mawrld-12}}
*{{Citation|last1=Varadarajan|first1=V. S.|title=The selected works of V. S. Varadarajan|url=https://books.google.com/books?id=0yOORTvBpYwC| publisher=[[American Mathematical Society]]|location=Providence, R.I. | isbn=978-0-8218-1068-2|mr=1647109| year=1999}}
*Varadarajan, Veeravalli S. (2004). Supersymmetry for mathematicians: an introduction. Vol. 11. American Mathematical Society.
* {{Cite book|url=http://bookstore.ams.org/euler|title=Euler Through Time: A New Look at Old Themes|last=Varadarajan|first=V. S.|year=2006|publisher=American Mathematical Society|isbn=9780821835807|language=en}}<ref>{{Cite journal|last=Roy|first=Ranjan|date=2008-01-01|title=Review of Euler Through Time: A New Look at Old Themes|jstor=27642523|journal=The American Mathematical Monthly|volume=115|issue=5|pages=469–473}}</ref>
* {{cite book| first2 = Rita | last2 = Fioresi | first1 = Sergio | last1 = Ferrara | first3 = Veeravalli S. | last3 = Varadarajan | title = Supersymmetry in Mathematics and Physics: UCLA Los Angeles, USA 2010 | publisher = Springer Verlag | year = 2011 | isbn = 978-3-642-21743-2 | doi = 10.1007/978-3-642-21744-9 |lccn = 2011934804}}
* {{cite book |url=https://www.springer.com/gp/book/9781441906663#aboutBook | last1=Varadarajan |first1=Veeravalli |title=Reflections on Quanta, Symmetries, and Supersymmetries |date=2011 |publisher=Springer-Verlag |isbn=978-1-4899-8944-4}}

== Selected publications ==
* Parthasarathy, K., Rao, R., & Varadarajan, V. (1967). Representations of Complex Semi-Simple Lie Groups and Lie Algebras. Annals of Mathematics, 85(3), second series, 383-429. doi:10.2307/1970351
*{{Citation | last1=Trombi | first1=P. C. | last2=Varadarajan | first2=V. S. | author2-link=Veeravalli S. Varadarajan | title=Spherical transforms of semisimple Lie groups | jstor=1970861 | mr=0289725 | doi = 10.2307/1970861 | year=1971 | journal=[[Annals of Mathematics]] | series=Second Series | volume=94 | issue=2 | pages=246–303}}.
* Enright, T., & Varadarajan, V. (1975). On an Infinitesimal Characterization of the Discrete Series. Annals of Mathematics, 102(1), second series, 1-15. doi:10.2307/1970970

==See also==
[[Born rule]]

==References==
{{Reflist}}

==External links==
*{{MathGenealogy|id=36691}}
*[https://www.math.ucla.edu/~vsv/ Home page of Veeravalli S. Varadarajan]
*[https://www.math.ucla.edu/news/memoriam-veeravalli-seshadri-varadarajan In Memoriam: Veeravalli Seshadri Varadarajan]
*[https://www.ias.ac.in/describe/article/reso/024/09/0941-0946 V S Varadarajan at the Indian Statistical Institute, Calcutta (K. R. Parthasarathy)]
*{{cite journal | last1 = Blasius | first1 = Don |last2=Digernes|first2=Trond |last3=Fioresi|first3=Rita |last4=Gangolli|first4=Ramesh|last5=Rapoport|first5=Michael |last6=Varadhan|first6=S. R. S. |date=October 2020| title = Recollections ofV. S. Varadarajan | journal = [[Notices of the American Mathematical Society]] | volume = 67| issue = 9 | pages = 1365–1373 | doi = 10.1090/noti2154 | url = https://www.ams.org/journals/notices/202009/rnoti-p1365.pdf |doi-access=free }}

{{Authority control}}

{{DEFAULTSORT:Varadarajan, Veeravalli S.}}
[[Category:1937 births]]
[[Category:2019 deaths]]
[[Category:20th-century Indian mathematicians]]
[[Category:Probability theorists]]
[[Category:University of California, Los Angeles faculty]]
[[Category:Indian Statistical Institute alumni]]
[[Category:21st-century Indian mathematicians]]
[[Category:Presidency College, Chennai alumni]]
[[Category:Fellows of the American Mathematical Society]]

Veeravalli S. Varadarajan - Revision history

->SdkbBot: Removed overlinked country wikilink and general fixes (task 2)