Isadore Singer connected analysis, topology and differential geometry. With Michael Atiyah, he proved the Atiyah-Singer index theorem, linking the analytic index of an elliptic operator to topological data.[ref]
https://www.maths.ox.ac.uk/node/31190. Institutional mathematical account of the joint index theorem
With Daniel Ray, he introduced analytic torsion using spectral information from Laplacians on differential forms. Their construction uses derivatives of spectral zeta functions to regularize otherwise divergent products of eigenvalues. The original paper proved invariance results and proposed equality with combinatorial torsion; that equality was a conjectural step in their paper.[ref]
R-torsion and the Laplacian on Riemannian manifolds by Daniel Ray and Isadore Singer. Introduction, Definition 1.6 and section 2
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Isadore Singer was an American mathematician, best known for his work in the fields of mathematics and theoretical physics, particularly in the areas of differential geometry, algebraic topology, and mathematical physics. He is renowned for co-developing the concept of the "Atiyah-Singer index theorem," which relates the analytical properties of differential operators to topological properties of manifolds. This theorem has had a profound impact on various areas of mathematics and theoretical physics.