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Abstract
Heat content is an invariant of piecewise smoothly bounded Riemannian domains. This talk is an introduction to heat content in the context of geometric analysis. Starting with definitions we will survey results which address the extent to which heat content of a domain determines the geometry of the domain. In particular, we compare and contrast the behavior of heat content and Dirichlet spectrum in the context of inverse problems. We present solutions to the inverse problem for several classes of polygonal domains.