= Juan Pablo Rossetti
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<Juan Pablo Rossetti> works on geometry and spectral questions. With Peter G. Doyle, he proved that closed <hyperbolic surfaces> with the same <Laplacian spectrum> have matching closed <geodesics>, separately counting orientation-preserving and orientation-reversing ones at each length.<Isospectral hyperbolic surfaces have matching geodesics by Peter G. Doyle and Juan Pablo Rossetti>[Original byline and Theorem 1]{ref}
The orientation distinction matters on nonorientable surfaces: different types of closed geodesic contribute differently to a trace formula. Their result explains exactly which geometric data can be recovered from the spectrum, extending the orientable setting of <Huber's theorem>.<Isospectral hyperbolic surfaces have matching geodesics by Peter G. Doyle and Juan Pablo Rossetti>[Sections 1–3]{ref}
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