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Monday, January 25, 2016

**Abstract:** Mark Kac's famous question 'Can you hear the shape of a drum?' is a question about how much geometry can we recover from the eigenvalues of the Laplacian on a compact manifold. One key invariant is the determinant of the Laplacian and I will explain how to define it given that the eigenvalues form an unbounded sequence. I will then explain what to do on some non-compact manifolds where the spectrum is uncountable.