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	'''Vijay Kumar Patodi''' (12 March 1945 – 21 December 1976) was an Indian [[mathematician]] who made fundamental contributions to [[differential geometry]] and [[topology]]. He was the first mathematician to apply heat equation methods to the proof of the [[~~Atiyah-Singer~~ index theorem\|~~Index Theorem~~]] for elliptic operators.{{citation needed\|date=March 2011}} He was a [[professor]] at [[Tata Institute of Fundamental Research]], [[Mumbai (Bombay)]].		'''Vijay Kumar Patodi''' (12 March 1945 – 21 December 1976) was an Indian [[mathematician]] who made fundamental contributions to [[differential geometry]] and [[topology]]. He was the first mathematician to apply [[heat equation]] methods to the proof of the [[Atiyah–Singer index theorem\|index theorem]] for elliptic operators.{{citation needed\|date=March 2011}} He was a [[professor]] at [[Tata Institute of Fundamental Research]], [[Mumbai (Bombay)]].

	==Education==		==Education==

>Simeon: Importing Wikidata short description: "Indian mathematician" (Shortdesc helper)

2021-04-08T17:51:35Z

Importing Wikidata short description: "Indian mathematician" (Shortdesc helper)

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{{Short description|Indian mathematician}}
{{Use Indian English|date=August 2015}}
{{Use dmy dates|date=August 2015}}
{{BLP sources|date=April 2011}}
{{Infobox scientist
| name = Vijay Kumar Patodi
| image = 
| image_size =
| alt =
| caption =
| birth_date = {{Birth date|df=yes|1945|03|12}}
| birth_place = [[Guna, India|Guna]], [[British India]] (now [[Madhya Pradesh]], [[India]])
| death_date = {{Death date and age|df=yes|1976|12|21|1945|03|12}}
| death_place = [[Bombay]], [[Maharashtra]]
| residence =
| citizenship =
| nationality = Indian
| fields =
| workplaces =
| alma_mater = [[Benaras Hindu University]]<br>[[University of Bombay]]<br>[[Institute for Advanced Study]]
| doctoral_advisor = [[M. S. Narasimhan]] <br> [[S. Ramanan]]
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for =
| author_abbrev_bot =
| author_abbrev_zoo =
| influences =
| influenced =
| awards = [[Young Scientist Award]]
| signature = 
| signature_alt =
| footnotes =
| spouse =
}}

'''Vijay Kumar Patodi''' (12 March 1945 – 21 December 1976) was an Indian [[mathematician]] who made fundamental contributions to [[differential geometry]] and [[topology]]. He was the first mathematician to apply heat equation methods to the proof of the [[Atiyah-Singer index theorem|Index Theorem]] for elliptic operators.{{citation needed|date=March 2011}} He was a [[professor]] at [[Tata Institute of Fundamental Research]], [[Mumbai (Bombay)]].

==Education==
Patodi was a graduate of Government High School, [[Guna, India|Guna]], [[Madhya Pradesh]]. He received his bachelor's degree from Vikram University, [[Ujjain]], his master's degree from the [[Benaras Hindu University]], and his Ph.D. from the [[University of Bombay]] under the guidance of M. S. Narasimhan and S. Ramanan at the [[Tata Institute of Fundamental Research]].<ref>{{Cite book
| url = https://books.google.com/books?id=TXje34eAhhEC&printsec=frontcover&cad=0#v=onepage&q&f=false
| title = Concise Biography
}}</ref>

In the two papers based on his Ph.D. thesis, "Curvature and Eigenforms of the Laplace Operator" (''Journal of Differential Geometry''), and "An Analytical Proof of the Riemann-Roch-Hirzebruch Formula for Kaehler Manifolds" (also ''Journal of Differential Geometry''), Patodi made his fundamental breakthroughs.<ref>{{Cite web
| url = http://vijay.com/other-vijays/vijay-patodi/
| title = Biography
}}</ref>

==Research career==
He was invited to spend 1971–1973 at the [[Institute for Advanced Study]] in [[Princeton, New Jersey|Princeton]], [[New Jersey]], where he collaborated with [[Michael Atiyah]], [[Isadore Singer]], and [[Raoul Bott]]. The joint work led to a series of papers, "Spectral Asymmetry and Riemannian Geometry" (''Math. Proc. Cambridge. Phil. Soc.'') with Atiyah and Singer, in which the [[η-invariant]] was defined. This invariant was to play a major role in subsequent advances in the area in the 1980s.<ref>{{Cite web
| url = http://www-history.mcs.st-and.ac.uk/Biographies/Patodi.html
| title = Biography
}}</ref>

Patodi was promoted to full professor at Tata Institute at age 30, however, he died at age 31, as a result of complications prior to surgery for a kidney transplant.

==References==
{{reflist}}

==External links==
* {{MacTutor Biography|id=Patodi}}
* {{MathGenealogy|id=35418}}
* [https://books.google.com/books?id=TXje34eAhhEC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Concise Biography]

{{Authority control}}

{{DEFAULTSORT:Patodi, Vijay Kumar}}
[[Category:20th-century Indian mathematicians]]
[[Category:Differential geometers]]
[[Category:Indian topologists]]
[[Category:Tata Institute of Fundamental Research alumni]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Vikram University alumni]]
[[Category:Banaras Hindu University alumni]]
[[Category:University of Mumbai alumni]]
[[Category:1945 births]]
[[Category:1976 deaths]]
[[Category:Scientists from Madhya Pradesh]]

{{India-scientist-stub}}
{{asia-mathematician-stub}}

Vijay Kumar Patodi - Revision history

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>Simeon: Importing Wikidata short description: "Indian mathematician" (Shortdesc helper)