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Duke Mathematical Journal, ISSN 0012-7094, 02/2012, Volume 161, Issue 3, pp. 415 - 429
We prove that every algebraic curve X/\overline{\mathbf{Q}} is birational over \mathbf{C} to a Teichmüller curve. This result is a corollary of our main... 
37D40 | 32G15
Journal Article
Michigan Math. J, 2015, Volume 64, Issue iss. 3, pp. 475 - 485
Journal Article
Mathematische Annalen, ISSN 0025-5831, 2/2019, Volume 373, Issue 1, pp. 1 - 36
The universal Teichmüller space is an infinitely dimensional generalization of the classical Teichmüller space of Riemann surfaces. It carries a natural... 
Mathematics, general | Secondary 32G15 | Mathematics | Primary 30F60 | MATHEMATICS
Journal Article
Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 2019, pp. 1 - 12
AbstractIn this we exploit the arithmeticity criterion of Oh and Benoist–Miquel to exhibit an origami in the principal stratum of the moduli space of... 
37D40 | 2010 Mathematics Subject Classification | 32G15
Journal Article
Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 2019, pp. 1 - 25
We describe in this article the dynamics of a one-parameter family of affine interval exchange transformations. This amounts to studying the directional... 
2010 Mathematics Subject Classification | 37E35 (Primary) | 57M50 | 32G15 (Secondary) | 37E05
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 07/2013, Volume 162, Issue 10, pp. 1833 - 1876
Let S be a surface of genus g with p Punctures with negative Euler characteristic. We study the diameter of the is an element of-thick part of moduli Space of... 
MATHEMATICS | TRIANGULATIONS | TEICHMULLER SPACE | GRAPHS | SURFACES | 05C85 | 32G15 | 20F34
Journal Article
Advances in Geometry, ISSN 1615-715X, 10/2019, Volume 19, Issue 4, pp. 505 - 526
Let 𝓜 be the moduli space of compact connected hyperbolic surfaces of genus ≥ 2, and 𝓑 ⊂ 𝓜 its branch locus. Let be the Deligne–Mumford compactification of... 
Primary 32G15 | stratification | noded Riemann surfaces | Moduli space | Secondary 14H10 | Loci | Strata
Journal Article
Mathematische Annalen, ISSN 0025-5831, 5/2012, Volume 353, Issue 1, pp. 1 - 35
In this paper, we investigate the closure of a large class of Teichmüller discs in the stratum $${\mathcal{Q}(1, 1, 1, 1)}$$ or equivalently, in a $${{\rm... 
57R30 | Mathematics, general | Primary 32G15 | Mathematics | Secondary 30F30 | 37D40 | Mathematics Subject Classification : Primary 32G15, Secondary 30F30, 57R30, 37D40
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 2/2018, Volume 192, Issue 1, pp. 207 - 243
We study the action of the group of polynomial automorphisms of $$\mathbb {C}^n (n \ge 3)$$ C n ( n ≥ 3 ) which preserve the Markoff–Hurwitz polynomial... 
Geometry | Polynomial automorphisms | 57M05 | 30F60 | 37F30 | Mathematics | 32G15 | Markoff–Hurwitz polynomial | Cayley graph | Identities | 20H10
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2005, Volume 127, Issue 2, pp. 291 - 311
In our paper [GSV], we discussed Poisson properties of cluster algebras of geometric type for the case of a nondegenerate matrix of transition exponents. In... 
MATHEMATICS | TRIANGULATIONS | SURFACES | 53D30 | 32G15 | 14M20 | 53D17
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 7/2019, Volume 39, Issue 4, pp. 1121 - 1135
Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are... 
moduli space | Strebel ray | Analysis | 30F60 | 30C62 | Mathematics, general | Teichmüller space | Mathematics | 32G15 | EDM ray | real hyper-elliptic subspace
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 10/2018, Volume 98, Issue 2, pp. 253 - 274
Marked Schottky space MSg is an explicit model of the quasiconformal deformation space of a Schottky group of rank g, this being isomorphic to the punctured... 
57M50 | 30F60 | 57M60 (secondary) | 32G15 | 30F10 | 30F40 (primary) | 57M10 | FORMS | MATHEMATICS | ABELIAN-VARIETIES | GENERATED KLEINIAN GROUPS | ALGEBRAIC-CURVES | MODULI SPACES | TEICHMULLER-SPACES | Mathematics - Complex Variables
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 8/2019, Volume 201, Issue 1, pp. 139 - 154
Let G be a finitely generated group of isometries of $$\mathbb {H}$$ H , hyperbolic 2-space. The discreteness problem is to determine whether or not G is... 
Poincaré Polygon Theorem | Roots | Mathematics | 32G15 | Topology | 30F35 | Convex and Discrete Geometry | Discreteness criteria | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Fuchsian group | Differential Geometry | 20H10
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 06/2018, Volume 97, Issue 3, pp. 398 - 426
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied... 
14N10 | 05A15 | 32G15 (primary) | MATHEMATICS | EQUATIONS | MODULI SPACE | COUNTING LATTICE POINTS | INVARIANTS | INTERSECTION THEORY
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2017, Volume 26, Issue 1, pp. 93 - 97
We describe a method to compute the norm on the cotangent space to the moduli space of Riemann surfaces associated to the Finsler Teichmüller metric. Our... 
Riemann surfaces | 32G15 | 30F30 | 30F60 | Teichmuller theory | MATHEMATICS | DISTANCE | CURVES | SURFACES
Journal Article
Mathematische Annalen, ISSN 0025-5831, 4/2018, Volume 370, Issue 3, pp. 1759 - 1787
This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface.... 
Secondary 30F60 | 53C22 | 58J50 | 11F72 | Mathematics, general | Primary 32G15 | Mathematics | 30F10 | MATHEMATICS | SIMPLE GEODESICS | ORBIFOLDS | SPACES | RIEMANN SURFACES | MANIFOLDS | MODULI
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 05/2018, Volume 38, Issue 3, pp. 950 - 964
The eventually distance minimizing ray (EDM ray) in moduli spaces of the Riemann surfaces of analytic finite type with 3g + n − 3 > 0 is studied, which was... 
32G15 | Strebel differential | augmented moduli space | EDM ray | Augmented Teichmüller space | 30F60 | Augmented Teichmuller space | MATHEMATICS | BEHAVIOR | DIFFERENTIALS
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 10/2016, Volume 181, Issue 2, pp. 501 - 502
In this erratum we correct a mistake in Yao (Monatsh Math. 178(2):311–324, 2015). 
30C75 | Open radius | Secondary 30C62 | Mathematics, general | Primary 32G15 | Mathematics | Strebel point
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 12/2018, Volume 197, Issue 1, pp. 193 - 227
We study two 2-dimensional Teichmuller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their... 
Teichmüller spaces | Convex hull | Divergence of geodesics | Extremal length | Exhaustion by polygons | MATHEMATICS | Teichmuller spaces | 30F60 | 32G15 | GEODESICS | SURFACES
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 9/2018, Volume 362, Issue 2, pp. 717 - 758
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | RIEMANN SURFACES | 3-MANIFOLDS | WEIL-PETERSSON | PHYSICS, MATHEMATICAL | MODULI SPACES | CHERN FORMS
Journal Article
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