Vijay Kumar Patodi

Vijay Kumar Patodi (12 March 1945-21 Dec 1976) born in Guna, India. Mathematical fame for Patodi came early in his career with papers of great importance coming for the work of his Ph.D. His doctoral thesis, Heat equation and the index of elliptic operators, was supervised by M S Narasimhan and S Ramanan and the degree was awarded by the University of Bombay in 1971.

Patodi's first paper Curvature and the eigenforms of the Laplace operator was part of his thesis. The second paper which came from his thesis was An analytic proof of the Riemann- Roch- Hirzebruch theorem for Kaehler manifolds which extended the methods of his first paper to a much more complicated situation.

The years 1971 to 1973 were ones which Patodi spent on leave at the Institute for Advanced Study at Princeton. There he worked with M F Atiyah and made several visits to work with others in his field at various centres in the United States and England. During this time he also collaborated with R Bott and I M Singer.

On his return to Bombay and the Tata Institute in 1973 Patodi was promoted to associate professor. He was promoted to full professor in 1976.

Patodi's publications, in addition to the two mentioned above, include a number of joint ones with Atiyah and Singer. These papers introduce a spectral invariant of a compact Riemannian manifold. In another paper he studies the relationship between Riemannian structures and triangulations. Other work gives a combinatorial formula for Pontryagin classes.

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