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Spectral decomposition and Siegel-Veech transforms for strata: The case of marked tori (with Jayadev Athreya, Jean Lagacé, Martin Raum) |
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arXiv: 2404.06597 |
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Latest version (pdf)
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| (52) |
A smooth compactification of spaces of stability conditions: the case of the An-quiver (with Anna Barbieri and Jeonghoon So) |
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arXiv: 2312.02686 |
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Latest Version (pdf)
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| (51) |
Teichmüller curves in hyperelliptic components of meromorphic strata (with Scott Mullane) |
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arXiv: 2305.03309 |
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Latest Version (pdf)
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| (50) |
Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients (with Matteo Costantini and Johannes Schwab) |
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arXiv: 2303.17929 |
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Latest Version (pdf)
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| (49) |
Quadratic differentials as stability conditions: collapsing subsurfaces (with Anna Barbieri, Yu Qiu and Jeonghoon So) |
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arXiv: 2212.08433 |
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Latest Version (pdf)
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| (48) |
A tale of two moduli spaces: logarithmic and multi-scale differentials (with Dawei Chen, Samuel Grushevsky, David Holmes and Johannes Schmitt) |
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arXiv: 2212.04704 |
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Latest Version (pdf)
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| (47) |
On the Kodaira dimension of moduli spaces of Abelian differentials (with Dawei Chen and Matteo Costantini) (April, 2022) |
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arXiv: 2204.11943 |
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Latest version (pdf)
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[Download] GP/Pari files for the computer assisted proofs:
onezerostrata, onezerobruteforce
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| (46) |
Compactifying the rank two Hitchin system via spectral data on semistable curves (with Johannes Horn) (arXiv: 2201.08104) |
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(to appear in Algebraic Geometry) |
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Latest Version (pdf)
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| (45) |
diffstrata -- A Sage package for calculations in the tautological ring of the moduli space of Abelian differentials (with Matteo Costantini and Jonathan Zachhuber) (arXiv: 2006.12815) |
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(Experimental Mathematics 32 (2023), no.3, 545-565) |
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Latest Version (pdf)
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| (44) |
The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials (with Matteo Costantini and Jonathan Zachhuber) (arXiv: 2006.12803) |
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(Forum of Mathematics, Pi, Volume 10, 2022) |
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Latest Version (pdf)
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| (43) |
Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials (with Dawei Chen, Adrien Sauvaget, with an appendix by Gaëtan Borot, Alessandro Giacchetto, Danilo Lewanski) (arXiv: 1912.02267) |
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(Duke Math. J. 172 (9), 1735-1779) |
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Latest Version (pdf)
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| (42) |
The area is a good enough metric (with Matteo Costantini and Jonathan Zachhuber) (arXiv: 1910.14151) |
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(to appear in Ann. Inst. Fourier) |
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Latest Version (pdf)
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| (41) |
The moduli space of multi-scale differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (October, 2019) |
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arXiv: 1910.13492 |
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Latest Version (pdf)
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| (40) |
Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials (with Dawei Chen, Adrien Sauvaget and Don Zagier)
arXiv: 1901.01785 |
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(Invent. Math. 222 (2020), no. 1, 283-373) |
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Latest Version (pdf)
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| (39) |
Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials (with Elise Goujard) (arXiv: 1809.05016) |
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(Algebr. Geom. Topol. 20 (2020), no. 5, 2451-2510) |
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Latest Version (pdf)
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| (38) |
Euler characteristics of Gothic Teichmüller curves. (with David Torres-Teigell) (arXiv: 1807.10260) |
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(Geom. Topol. 24 (2020), no. 3, 1149-1210) |
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Latest Version (pdf)
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| (37) |
Realizability of tropical canonical divisors (with Martin Ulirsch and Annette Werner) (arXiv: 1710.06401) |
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(J. Eur. Math. Soc. 23 (2021), no. 1, 185-217) |
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Latest Version (pdf)
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| (36) |
Cones of Heegner divisors (with Jan Hendrik Bruinier) (arXiv: 1705.05534) |
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(J. Algebraic Geom. 28 (2019), 497-517) |
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Latest Version (pdf)
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| (35) |
Non-existence and finiteness results for Teichmueller curves in Prym loci (with Erwan Lanneau) (arXiv: 1704.03210) |
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(Experimental Mathematics 31 (2022), no. 2, 621-636) |
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Latest Version (pdf)
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[Download] GP/Pari files and sage files for the computer assisted proofs:
prym22_equation, prym211_equation,
Section_6.1.sage, Section_6.2.sage and Section_8.2.sage#mce_temp_url#
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Strata of k-differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (arXiv: 1610.09238) |
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(Algebr. Geom. 6 (2019), no. 2, 196–233) |
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Latest Version (pdf)
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| (33) |
Counting Feynman-like graphs: Quasimodularity and Siegel-Veech weight (with Elise Goujard) (arXiv: 1609.01658) |
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(J. Europ. Math. Soc. 22 (2020), 365-412) |
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Latest Version (pdf)
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| (32) |
Lower bounds for Lyapunov exponents of flat bundles on curves (with Alex Eskin, Maxim Kontsevich and Anton Zorich) (arXiv: 1609.01170) |
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(Geom. Topol. 22 (2018), no. 4, 2299–2338) |
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Latest Version (pdf)
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| (31) |
Quasimodularity and large genus limits of Siegel-Veech constants (with Dawei Chen and Don Zagier) (arXiv:1606.04065) |
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(J. Amer. Math. Soc. 31 (2018), no. 4, 1059–1163) |
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Latest Version (pdf)
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| (30) |
Compactification of strata of abelian differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (arXiv:1604.08834) |
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(Duke Math. J. 167 (2018), no. 12, 2347–2416) |
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Latest Version (pdf)
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| (29) |
Explicit formulas for infinitely many Shimura curves in genus 4 (with Samuel Grushevsky) (arXiv:1510_05674) |
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(Asian J. Math. 22 (2018), no. 2, 381–390) |
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Latest Version (ps) Latest Version (pdf)
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| (28) |
Cutting out arithmetic Teichmüller curves in genus two via Theta functions (with André Kappes) (arXiv:1504.00470) |
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(Comment. Math. Helv. 92 (2017), 257–309) |
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Latest Version (pdf)
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| (27) |
Modular embeddings of Teichmüller curves (with Don Zagier) (arXiv:1503.05690) |
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(Compositio Math. 152 (2016), 2269-2349) |
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Latest Version (ps) Latest Version (pdf)
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| (26) |
Teichmüller curves in genus three and just likely intersections in Gnm × Gna (with Matt Bainbridge and Philipp Habegger) (arXiv:1410.6835) |
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(Publ. Math. IHES, Vol. 124 No. 1 (2016), 1-98) |
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Latest Version (pdf)
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[Download] Sage file for the computer assisted proofs: g3fin_ch6.sage and g3fin_ch9.sage |
| (25) |
Bounded negativity of self-intersection numbers of shimura curves on shimura surfaces (with Domingo Toledo) (arXiv:1407.5181) |
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(Algebra and Number Theory 9-4 (2015), 897-912) |
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Latest Version (pdf)
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| (24) |
Shimura curves within the locus of genus3 hyperelliptic curves (with Samuel Grushevsky) (arXiv:1308.5155) |
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(Int Math Res Notices (2016) Vol. 2016 1603-1639) |
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Latest Version (ps) Latest Version (pdf)
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| (23) |
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (with Carlos Matheus and Jean-Christophe Yoccoz) (arXiv:1305.2033) |
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(Invent. Math. 202 (2013), 333-425) |
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Latest Version (pdf)
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| (22) |
Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle (with Artur Avila and Alex Eskin) (arXiv:1209.2854) |
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(J. Reine Angew. Math. 732 (2017), 1–20) |
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Latest Version (ps) Latest Version (pdf)
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| (21) |
Lyapunov spectrum of ball quotients with applications to commensurability questions (with Andre Kappes) (arXiv:1207.5433) |
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(Duke Math. Journal, 165 (2016), 1-66) |
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Latest Version (ps) Latest Version (pdf)
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| (20) |
Quadratic differentials in low genus: exceptional and non-varying (with Dawei Chen) (arXiv:1204.1707) |
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(Ann. Sci. ENS 47 (2014), 309–370) |
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Latest Version (ps) Latest Version (pdf)
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| (19) |
Prym covers, theta functions and Kobayashi geodesics in Hilbert modular surfaces |
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(Amer. Journal. of Math. 136 (2014), 995–1022) |
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Latest Version (ps) Latest Version (pdf)
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| (18) |
The locus of real multiplication and the Schottky locus (with Matt Bainbridge) (arXiv:1107.3832) |
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(J. Reine Angew. Math. 685 (2014), 167-186) |
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Latest Version (ps) Latest Version (pdf)
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| (17) |
Non-varying sums of Lyapunov exponents of Abelian differentials in low genus (with Dawei Chen) (arXiv: 1104.3932) |
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(Geometry and Topology 12 (2012), 101-154) |
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Latest Version (ps) Latest Version (pdf)
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| (16) |
Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant (with A. Pohl) ( math.DS/1103.5235) |
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(Erg.Th.Dyn.Syst. 33 (2013), 247-283) |
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Latest Version (ps) Latest Version (pdf)
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| (15) |
The Deligne-Mumford-compactification of Hilbert modular varieties and Teichmueller curves in genus three (with Matt Bainbridge) (math.AG/0911.4677) |
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(Acta Math. 208 (2012), 1-92) |
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Latest Version (ps) Latest Version (pdf)
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| (14) |
Kobayashi geodesics in A_g (with Eckart Viehweg) (math.AG/0809.1018) |
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(Journal of Diff. Geom 86 Nr. 2 (2011), 355--379) |
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Latest Version (ps) Latest Version (pdf)
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| (13) |
Differential equations associated with nonarithmetic Fuchsian groups (with Irene Bouw) ( math.AG/0710.5277) |
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(Journal London Math. Soc. 81 No. 1 (2010), 65-90) |
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Latest Version (ps) Latest Version (pdf)
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| (12) |
Completely periodic directions and orbit closures of many pseudo-Anosov Teichmüller discs in Q(1,1,1,1)
(with Pascal Hubert and Erwan Lanneau) (math.AG/0707.0738) |
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(Math. Ann 353 (2012), 1-35) |
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Latest Version (ps) Latest Version (pdf)
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| (11) |
Stability of Hodge bundles and a numerical characterization of Shimura varieties (with Eckart Viehweg and Kang Zuo) (Mathematics arXiv: math.AG/0706.3462) |
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(Journ. Diff. Geom. 92 (2012), 71-151) |
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Latest Version (ps) Latest Version (pdf)
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| (10) |
Linear manifolds in the moduli space of one-forms (math.AG/0703145) |
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(Duke Math. J. 144 No.3 (2008), 447-488) |
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Latest Version (ps) Latest Version (pdf)
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| (9) |
The Arnoux-Yoccoz Teichmüller disc (with Pascal Hubert and Erwan Lanneau) (math.AG/0611655) |
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(GAFA 18 No. 6 (2008), 1988-2016) |
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Latest Version (ps) Latest Version (pdf)
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| (8) |
Teichmüller curves, triangle groups, and Lyapunov exponents (with Irene Bouw) (math.AG/0511738) |
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(Annals of Math. 172 (2010), 139-185) |
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Latest Version (ps) Latest Version (pdf) (math.AG/0509079)
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| (7) |
Finiteness results for Teichmueller curves |
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(Ann. Inst. Fourier 58 (2008), 63-83) |
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Latest Version (ps) Latest Version (pdf)
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| (6) |
Shimura- and Teichmueller curves (math.AG/0501333) |
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(Journal Modern Dynamics 5 No.1 (2011),1-32) |
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Latest Version (ps) Latest Version (pdf)
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| (5) |
Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmueller curve (math.AG/0410262) |
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(Invent. Math. 165 No. 3 (2006), 633-649) |
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Latest Version (ps) Latest Version (pdf)
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| (4) |
Variations of Hodge structure of Teichmueller curves (math.AG/0401290) |
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(Journal of the AMS 19 (2006), 327-344) |
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Latest Version (ps) Latest Version (pdf)
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| (3) |
Teichmueller curves, Galois actions and GT-relations (math.AG/0311308) |
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(Math. Nachrichten 278 No. 9 (2005),1061–1077) |
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Latest Version (ps) Latest Version (pdf)
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| (2) |
Isotrivially fibred isles in the moduli space of surfaces of general type (math.AG/0210318) |
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(Proc. AMS 133 No.2 (2005),357–362) |
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Latest Version (ps) Latest Version (pdf)
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| (1) |
Maximally irregularly fibred surfaces of general type (math.AG/0209120) |
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(Manusc. Math. 116 (2005),71–92) |
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Latest Version (ps) Latest Version (pdf) |
