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Alexander Strohmaier studies global analysis, spectral geometry and quantum field theory in curved spacetime. His Hannover research page connects spectra of geometric differential operators with classical dynamics.^[ref]

With Emily B. Dryden, he extended Huber's theorem to compact orientable hyperbolic orbisurfaces: the Laplacian spectrum determines the lengths of closed geodesics and the number of singular points of each order, with a converse. The result uses a Selberg trace formula to relate spectral and geometric terms.^[ref]

Emily B. Dryden studies spectral geometry: the relationship between geometric spaces and spectra of differential operators. Her Bucknell profile identifies this research specialization.^[ref]

With Alexander Strohmaier, she proved an orbisurface version of Huber's theorem. For compact orientable hyperbolic orbisurfaces, the Laplacian spectrum determines both closed-geodesic lengths and singular-point orders with multiplicities; the corresponding geometric data also determine the spectrum. Thus spectral information records some singular geometry as well as ordinary closed paths.^[ref]