Decay of L^2-harmonic forms via microlocal methods

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I will explain a general and flexible method originally introduced by Richard Melrose for estimating the decay of L^2-harmonic forms at infinity, but focusing on the specific example of L^2-harmonic forms of fibered boundary metrics (e.g. most types of gravitational instantons), in which case the result is due to Hausel-Hunsicker-Mazzeo in 2004 and heavily relies on the parametrix construction of Vaillant.  After outlining the method, I will introduce the pseudodifferential calculus needed and describe  the important steps of the parametrix construction.  I will also indicate other important results that can be obtained with this method.

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