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 index theorem for elliptic operators.
[1] 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.
[2] He was invited to spend 1971–1973 at the Institute for Advanced Study 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" with Atiyah and Singer,[3][4][5] in which the η-invariant was defined.