= Isadore Singer
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<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.https://www.maths.ox.ac.uk/node/31190[Institutional mathematical account of the joint index theorem]{ref}
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.<R-torsion and the Laplacian on Riemannian manifolds by Daniel Ray and Isadore Singer>[Introduction, Definition 1.6 and section 2]{ref}
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