Geodesic
Translation surfaces: Dynamics and Hodge theory
Simion Filip1
1University of Chicago, Chicago, USA
EMS surveys in mathematical sciences, Tome 11 (2024) no. 1, pp. 63-151

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DOI

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.
DOI : 10.4171/emss/78
Classification : 32G20, 14D07, 14H15, 32G15, 37E35, 37F34
Mots-clés : translation surfaces, Hodge theory, moduli spaces, abelian differentials, dynamics on surfaces, measure rigidity

Simion Filip  1

1 University of Chicago, Chicago, USA 
Simion Filip. Translation surfaces: Dynamics and Hodge theory. EMS surveys in mathematical sciences, Tome 11 (2024) no. 1, pp. 63-151. doi: 10.4171/emss/78
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     number = {1},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/78/}
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