I will give an overview of recent developments in the study of Hardy-type inequalities on manifolds and on graphs. In particular, I will present a technique to get 'as large as possible' Hardy weights which is made precise by the notion of optimality. Moreover, I will restrict myself to Laplacians on smooth manifolds and bounded combinatorial graphs, although the results remain true in far greater generality. This talk will summarise a survey paper by Keller, Pinchover and Pogorzelski (2020).
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