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Translation surfaces: dynamics and Hodge theory - MaRDI portal

Translation surfaces: dynamics and Hodge theory (Q6545225)

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scientific article; zbMATH DE number 7854808

Language	Label	Description	Also known as
English	Translation surfaces: dynamics and Hodge theory	scientific article; zbMATH DE number 7854808

Statements

scholarly article

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Translation surfaces: dynamics and Hodge theory (English)

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EMS Surveys in Mathematical Sciences

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publication date

29 May 2024

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zbMATH Keywords

translation surfaces

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moduli spaces

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MaRDI profile type

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The Betti map associated to a section of an abelian scheme

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\(\mathrm{GL}_2\mathbb{R}\) orbit closures in hyperelliptic components of strata

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Moduli spaces of complex affine and dilation surfaces

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High rank invariant subvarieties

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Residues of connections and the Chevalley-Weil formula for curves

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Deviation of ergodic averages for rational polygonal billiards

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Classification of higher rank orbit closures in \(\mathcal{H}^{\mathrm{odd}}(4)\)

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Symplectic and isometric \(\mathrm{SL}(2,\mathbb{R})\)-invariant subbundles of the Hodge bundle

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Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

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Arithmeticity, superrigidity, and totally geodesic submanifolds

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Boundaries, rigidity of representations, and Lyapunov exponents

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Compactification of strata of abelian differentials

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Strata of $k$-differentials

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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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Haupt's theorem for strata of abelian differentials

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The Deligne-Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3

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On the distribution of the Hodge locus

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Equations of linear subvarieties of strata of differentials

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Stationary measures and closed invariants on homogeneous spaces

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Stationary measures and invariant subsets of homogeneous spaces (II)

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Connected components of the strata of the moduli space of meromorphic differentials

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Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group

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Teichmüller curves, triangle groups, and Lyapunov exponents

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Framed mapping class groups and the monodromy of strata of abelian differentials

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A transfer principle: from periods to isoperiodic foliations

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Veech surfaces and complete periodicity in genus two

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The horocycle flow on the moduli space of translation surfaces

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Teichm\"uller dynamics in the eyes of an algebraic geometer

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AFFINE GEOMETRY OF STRATA OF DIFFERENTIALS

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The irreducibility of the space of curves of a given genus

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Ratner's theorem on \(\mathrm{SL}(2,\mathbb R)\)-invariant measures

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On measures invariant under diagonalizable actions: the rank-one case and the general low-entropy method

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Arithmetic Veech sublattices of SL\((2,\mathbf {Z})\)

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The algebraic hull of the Kontsevich-Zorich cocycle

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A coding-free simplicity criterion for the Lyapunov exponents of Teichmüller curves

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Billiards, quadrilaterals and moduli spaces

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Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space

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Isolation, equidistribution, and orbit closures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space

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Semisimplicity and rigidity of the Kontsevich-Zorich cocycle

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Splitting mixed Hodge structures over affine invariant manifolds

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Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle

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Notes on the multiplicative ergodic theorem

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Counting special lagrangian fibrations in twistor families of K3 surfaces

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Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups

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Canonical currents and heights for K3 surfaces

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Gaps in the support of canonical currents on projective K3 surfaces

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Deviation of ergodic averages for area-preserving flows on surfaces of higher genus

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Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards

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Concerning the transitive properties of geodesics on a rational polyhedron.

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Topics in Transcendental Algebraic Geometry. (AM-106)

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Flat surfaces and stability structures

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Ein Satz über die Abelschen Integrale 1. Gattung.

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Grid Graphs and Lattice Surfaces

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Periods of abelian differentials and dynamics

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Ergodicity of billiard flows and quadratic differentials

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Bi-algebraic geometry and the André-Oort conjecture

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Connected components of the moduli spaces of Abelian differentials with prescribed singularities

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Real multiplication through explicit correspondences

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Periods of Abelian Differentials With Prescribed Singularities

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Invariant measures and arithmetic unique ergodicity. Appendix by E. Lindenstrauss and D. Rudolph

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ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES

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The fine structure of the moduli space of abelian differentials in genus 3

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Interval exchange transformations and measured foliations

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Hausdorff dimension of the set of nonergodic foliations of a quadratic differential

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A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces

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Billiards and Teichmüller curves on Hilbert modular surfaces

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Prym varieties and Teichmüller curves

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Teichmüller curves in genus two: Torsion divisors and ratios of sines

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Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two

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Teichmüller dynamics and unique ergodicity via currents and Hodge theory

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Billiards, heights, and the arithmetic of non-arithmetic groups

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Billiards and Teichmüller curves

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Nondivergence of horocyclic flows on moduli space

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The boundary of an affine invariant submanifold

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Full-rank affine invariant submanifolds

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Teichmüller curves, Galois actions and $ \widehat {GT} $‐relations

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Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve

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Variations of Hodge structures of a Teichmüller curve

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Linear manifolds in the moduli space of one-forms

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GEOMETRY OF TEICHMÜLLER CURVES

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On Raghunathan's measure conjecture

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Categories tannakiennes

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Survey lecture on billiards

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Minimal sets for flows on moduli space

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Chamber structure of modular curves \(X_1(N)\)

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On the ergodicity of flat surfaces of finite area

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Gauss measures for transformations on the space of interval exchange maps

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The Teichmüller geodesic flow

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Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards

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Moduli spaces of quadratic differentials

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The field of definition of affine invariant submanifolds of the moduli space of abelian differentials

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Cylinder deformations in orbit closures of translation surfaces

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Translation surfaces and their orbit closures: an introduction for a broad audience

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Identifiers

zbMATH Open document ID

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10.4171/emss/78

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6545225

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