@inbook{1468, abstract = {This chapter surveys the motivations, related results, and progress made towards the following problem, raised by Hitchin in 1995: What is the space of L2 harmonic forms on the moduli space of Higgs bundles on a Riemann surface?}, author = {Tamas Hausel}, booktitle = {The Many Facets of Geometry: A Tribute to Nigel Hitchin}, publisher = {Oxford University Press}, title = {{S-Duality in HyperkäHler Hodge Theory}}, doi = {10.1093/acprof:oso/9780199534920.003.0016}, year = {2010}, }