Veeravalli S. Varadarajan | |
---|---|

Born | Bengalaru, India ^{[1]} | 18 May 1937

Died | 25 April 2019 Santa Monica, California, U.S. | (aged 81)

Nationality | Indian |

Alma mater | Loyola College, Madras Presidency College, Madras Indian Statistical Institute, Kolkata |

Known for | Trombi–Varadarajan theorem |

Awards | Onsager Medal |

Scientific career | |

Fields | Mathematics |

Institutions | University of California, Los Angeles Indian Statistical Institute, Kolkata |

Doctoral advisor | C. R. Rao |

**Veeravalli Seshadri ^{[2]} Varadarajan** (18 May 1937 – 25 April 2019)

^{[3]}

^{[4]}

^{[5]}was an Indian mathematician at the University of California, Los Angeles, who worked in many areas of mathematics, including probability, Lie groups and their 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, Madras where he was taught mathematics by K.A. Adivarahan, a very strict disciplinarian who made a strong impression on him.^{[1]}^{[6]} Varadarajan received his undergraduate degree in 1957 from Presidency College, Madras and his doctorate in 1960 from the Indian Statistical Institute in Calcutta, under the supervision of C. R. Rao.^{[7]} He was one of the "famous four"^{[8]} at the Indian Statistical Institute during 1956-1963 (the others being
R. Ranga Rao, 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.^{[9]} 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.^{[10]} 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.^{[11]}

## 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 determinants along with Bertram Kostant, K. R. Parthasarathy and R. Ranga Rao in 1967,^{[12]} the Trombi–Varadarajan theorem^{[13]} in 1972 and the Enright–Varadarajan modules^{[14]} 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.^{[15]}

## Bibliography

- Varadarajan, Veeravalli S (1984). Geometry of quantum theory, Springer-Verlag. 1st Edition 1968.
- Varadarajan, V. S. (1984),
*Lie groups, Lie algebras, and their representations*, Springer Verlag, ISBN 978-0387909691;*1st edition*. 1974.^{[16]} - Varadarajan, V. S. (1977),
*Harmonic analysis on real reductive groups*, Springer-Verlag^{[17]} - Gangolli, Ramesh; Varadarajan, V. S. (1983),
*Harmonic analysis of spherical functions on real reductive groups*, Springer-Verlag^{[18]} - Varadarajan, V. S. (1999),
*An Introduction to Harmonic Analysis on Semisimple Lie Groups*, Cambridge University Press, ISBN 9780521663625;*1st edition*. 1989.^{[19]} - Varadarajan, V. S. (1998),
*Algebra in Ancient and Modern Times*, AMS & Hindustan Book Agency - Varadarajan, V. S. (1999),
*The selected works of V. S. Varadarajan*, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1068-2, MR 1647109 - Varadarajan, Veeravalli S. (2004). Supersymmetry for mathematicians: an introduction. Vol. 11. American Mathematical Society.
- Varadarajan, V. S. (2006).
*Euler Through Time: A New Look at Old Themes*. American Mathematical Society. ISBN 9780821835807.^{[20]} - Ferrara, Sergio; Fioresi, Rita; Varadarajan, Veeravalli S. (2011).
*Supersymmetry in Mathematics and Physics: UCLA Los Angeles, USA 2010*. Springer Verlag. doi:10.1007/978-3-642-21744-9. ISBN 978-3-642-21743-2. LCCN 2011934804. - Varadarajan, Veeravalli (2011).
*Reflections on Quanta, Symmetries, and Supersymmetries*. 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

- Trombi, P. C.; Varadarajan, V. S. (1971), "Spherical transforms of semisimple Lie groups",
*Annals of Mathematics*, Second Series,**94**(2): 246–303, doi:10.2307/1970861, JSTOR 1970861, MR 0289725.

- 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

## References

- ^
^{a}^{b}"Reflections on a Long Innings – Bhāvanā". Retrieved 30 July 2019. **^**http://www.worldcat.org/identities/lccn-n50044956/**^**http://id.loc.gov/authorities/names/n50044956.html**^**https://www.math.ucla.edu/news/memoriam-veeravalli-seshadri-varadarajan**^**https://www.ias.ac.in/public/Volumes/reso/024/09/0941-0946.pdf**^**"V.S. Varadarajan: Reflections on a Long Innings".*The Wire*. Retrieved 30 July 2019.**^**https://www.genealogy.math.ndsu.nodak.edu/id.php?id=36691**^**Sinha, Kalyan Bidhan; Bhat, B. V. Rajarama. "Veeravalli S. Varadarajan" (PDF). Louisiana State University.**^**Varadarajan, V. S. (2011).*Reflections on Quanta, Symmetries, and Supersymmetries*. Springer-Verlag. pp. 8–10.**^**https://www.ias.edu/scholars/veeravalli-s-varadarajan**^**http://newsroom.ucla.edu/releases/professor-emeritus-gives-1-million-to-bring-visiting-mathematics-faculty-to-ucla**^**Parthasarathy, K. R.; Rao, R. Ranga; Varadarajan, V. S. (1967). "Representations of complex semi-simple Lie groups and Lie algebras".*Annals of Mathematics*.**85**(3): 383–429. doi:10.2307/1970351. JSTOR 1970351.**^**Trombi, P. C.; Varadarajan, V. S. (1972). "Asymptotic behaviour of eigen functions on a semisimple Lie group: The discrete spectrum".*Acta Mathematica*.**129**(1): 237–280. doi:10.1007/bf02392217.**^**Enright, Thomas J.; Varadarajan, V. S. (1975). "On an infinitesimal characterization of the discrete series".*Annals of Mathematics*.**102**(1): 1–15. doi:10.2307/1970970. JSTOR 1970970.**^**"American Mathematical Society Honors 23 Indians".*Nov 1, 2012*. India-West. Archived from the original on 23 December 2012. Retrieved 19 December 2012.CS1 maint: unfit URL (link)**^**Knapp, A. W. (1975). "Review:*Lie groups, Lie algebras, and their representations*, by V. S. Varadarajan; and*Compact Lie groups and their representations*, by D. P. Želobenko" (PDF).*Bull. Amer. Math. Soc. (N.S.)*.**81**(5): 865–872. doi:10.1090/s0002-9904-1975-13866-3.**^**Herb, Rebecca A. (1979). "Review:*Harmonic analysis on real reductive groups*, by V. S. Varadarajan" (PDF).*Bull. Amer. Math. Soc. (N.S.)*.**1**(2): 398–401. doi:10.1090/s0273-0979-1979-14614-7.**^**Barbasch, D. (1990). "Review:*Harmonic analysis of spherical functions on real reductive groups*, by R. Gangolli and V. S. Varadarajan" (PDF).*Bulletin of the American Mathematical Society*. (N.S.).**23**(2): 598–604. doi:10.1090/s0273-0979-1990-15996-8.**^**Wolf, Joseph A. (1993). "Review:*An introduction to harmonic analysis on semisimple Lie groups*, by V. S. Varadarjan" (PDF).*Bulletin of the American Mathematical Society*. (N.S.).**28**(2): 367–370. doi:10.1090/s0273-0979-1993-00365-3.**^**Roy, Ranjan (1 January 2008). "Review of Euler Through Time: A New Look at Old Themes".*The American Mathematical Monthly*.**115**(5): 469–473. JSTOR 27642523.

## External links

- Veeravalli S. Varadarajan at the Mathematics Genealogy Project
- Home page of Veeravalli S. Varadarajan
- In Memoriam: Veeravalli Seshadri Varadarajan
- V S Varadarajan at the Indian Statistical Institute, Calcutta (K. R. Parthasarathy)
- Blasius, Don; Digernes, Trond; Fioresi, Rita; Gangolli, Ramesh; Rapoport, Michael; Varadhan, S. R. S. (October 2020). "Recollections ofV. S. Varadarajan" (PDF).
*Notices of the American Mathematical Society*.**67**(9): 1365–1373. doi:10.1090/noti2154.