Abstract
In our recent works (Grushevsky and Krichever, The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces. In: Surveys in differential geometry. Vol. XIV. Geometry of Riemann surfaces and their moduli spaces. Volume 14 of surveys in differential geometry. International Press, Somerville, pp 111–129, 2009; Grushevsky and Krichever, Foliations on the moduli space of curves, vanishing in cohomology, and Calogero-Moser curves, arXiv:1108.4211, part 1, under revision) we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how they are related to and motivated by the spectral theory of the elliptic Calogero-Moser integrable system.
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