Wednesday, May 1, 2019 - 12:00pm to 1:00pm

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Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

We present two graph quantities ψ(G,S) and ψ2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues of the Laplacian, λ(G,S) and λ2(G), respectively. These quantities are “electrical" relaxations of the sparsest cut on a graph and our main theorem gives an “electrical” alternative to Cheeger’s inequality. Along the way we will talk about spring-mass systems and Muckenhoupt’s weighted Hardy inequality.

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