Translation surfaces: dynamics and Hodge theory

Compact Riemann surfaces and uniformization (30F10) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15)

Cites Work

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On the distribution of the Hodge locus
Survey lecture on billiards
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Splitting mixed Hodge structures over affine invariant manifolds
Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
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Teichmüller curves in genus three and just likely intersections in $\mathbf{G}_{m}^{n}\times\mathbf{G}_{a}^{n}$
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Stationary measures and closed invariants on homogeneous spaces
Flat surfaces and stability structures
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Moduli spaces of quadratic differentials
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A coding-free simplicity criterion for the Lyapunov exponents of Teichmüller curves
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Deviation of ergodic averages for rational polygonal billiards
Linear manifolds in the moduli space of one-forms
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Ratner's theorem on $\mathrm{SL}(2,\mathbb R)$-invariant measures
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The Teichmüller geodesic flow
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Hausdorff dimension of the set of nonergodic foliations of a quadratic differential
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The algebraic hull of the Kontsevich-Zorich cocycle
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Symplectic and isometric $\mathrm{SL}(2,\mathbb{R})$-invariant subbundles of the Hodge bundle
Full-rank affine invariant submanifolds
Minimal sets for flows on moduli space
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The Betti map associated to a section of an abelian scheme
Arithmeticity, superrigidity, and totally geodesic submanifolds
Equations of linear subvarieties of strata of differentials
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Cylinder deformations in orbit closures of translation surfaces
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Teichm\"uller dynamics in the eyes of an algebraic geometer
Nondivergence of horocyclic flows on moduli space
Veech surfaces and complete periodicity in genus two
Stationary measures and invariant subsets of homogeneous spaces (II)
Periods of Abelian Differentials With Prescribed Singularities
GEOMETRY OF TEICHMÜLLER CURVES
Billiards, quadrilaterals and moduli spaces
Bi-algebraic geometry and the André-Oort conjecture
Strata of $k$-differentials
AFFINE GEOMETRY OF STRATA OF DIFFERENTIALS
Grid Graphs and Lattice Surfaces
ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES
Boundaries, rigidity of representations, and Lyapunov exponents
Teichmüller curves, Galois actions and $ \widehat {GT} $‐relations
Notes on the multiplicative ergodic theorem
Billiards and Teichmüller curves
Framed mapping class groups and the monodromy of strata of abelian differentials