Translation surfaces: Dynamics and Hodge theory

  • Simion Filip

    University of Chicago, Chicago, USA
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Abstract

A translation surface is a multifaceted object that can be studied with the tools of dynamics, analysis, or algebraic geometry. Moduli spaces of translation surfaces exhibit equally rich features. This survey provides an introduction to the subject and describes some developments that make use of Hodge theory to establish algebraization and finiteness statements in moduli spaces of translation surfaces.

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Simion Filip, Translation surfaces: Dynamics and Hodge theory. EMS Surv. Math. Sci. 11 (2024), no. 1, pp. 63–151

DOI 10.4171/EMSS/78