Vijay Kumar Patodi
Encyclopedia
Vijay Kumar Patodi was an India
n 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 Index Theorem for elliptic operators. He was a professor
at Tata Institute of Fundamental Research
, Mumbai (Bombay).
, 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
.
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.
in 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
-invariant was defined. This invariant was to play a major role in subsequent advances in the area in the 1980s.
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.
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who made fundamental contributions to differential geometry and topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
. He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators. He was a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at Tata Institute of Fundamental Research
Tata Institute of Fundamental Research
The Tata Institute of Fundamental Research is a research institution in India dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the Department of Atomic Energy of the Government of India. It is located at Navy Nagar, Colaba, Mumbai...
, Mumbai (Bombay).
Education
Patodi was a graduate of Government High School, GunaGuna
' means 'string' or 'a single thread or strand of a cord or twine'. In more abstract uses, it may mean 'a subdivision, species, kind, quality', or an operational principle or tendency....
, Madhya Pradesh
Madhya Pradesh
Madhya Pradesh , often called the Heart of India, is a state in central India. Its capital is Bhopal and Indore is the largest city....
. He received his bachelor's degree from Vikram University, Ujjain
Ujjain
Ujjain , is an ancient city of Malwa region in central India, on the eastern bank of the Kshipra River , today part of the state of Madhya Pradesh. It is the administrative centre of Ujjain District and Ujjain Division.In ancient times the city was called Ujjayini...
, 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
Tata Institute of Fundamental Research
The Tata Institute of Fundamental Research is a research institution in India dedicated to basic research in mathematics and the sciences. It is a Deemed University and works under the umbrella of the Department of Atomic Energy of the Government of India. It is located at Navy Nagar, Colaba, Mumbai...
.
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.
Research career
He was invited to spend 1971–1973 at the Institute for Advanced StudyInstitute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
, where he collaborated with Michael Atiyah
Michael Atiyah
Sir Michael Francis Atiyah, OM, FRS, FRSE is a British mathematician working in geometry.Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study...
, Isadore Singer
Isadore Singer
Isadore Manuel Singer is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology...
, and Raoul Bott
Raoul Bott
Raoul Bott, FRS was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense...
. 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
-invariant was defined. This invariant was to play a major role in subsequent advances in the area in the 1980s.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.