May - August 2010
Organizers: Alex Eskin, Ursula Hamenstädt, Maxim Kontsevich, Martin Möller, Jean-Christophe Yoccoz, and Anton Zorich
Description: In recent years, there was tremendous progress in this research area which is partially due to the impact of researchers whose primary expertise is outside the area. Methods which became increasingly important are dynamics of Lie group actions, symbolic dynamics or algebraic geometric tools. Among spectacular examples one can mention the solution of the Kontsevich-Zorich conjecture by Avila and Viana or the classification theorem of McMullen in genus two. On the other hand, many young extremely talented people began to work in this area bringing in new unconventional ideas.
This Hausdorff Trimester Program brought together leading senior researchers representing the different aspects of this area as well as a considerable number of young people, including graduate students.
Associated Events: Workshop: Subgroups of mapping class groups
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| No. | Author(s) | Title | Preprint | Publication |
| 2010b01 | Bugeaud, Y.; Hubert, P.; Schmidt, T. A. | Transcendence with Rosen continued fractions | 1007.2050 | J. Eur. Math. Soc. 15(1) (2013), 39–51. https://doi.org/10.4171/JEMS/355 |
| 2010b02 | Basmajian, A. | Universal length bounds for non-simple closed geodesics on hyperbolic surfaces | J. Topol. 6(2) (2013), 513–524. https://doi.org/10.1112/jtopol/jtt005 |
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| 2010b03 | Calegari, D.; Maher, J. | Statistics and compression of scl | 1008.4952 | Ergodic Theory Dynam. Systems. 35(1) (2015), 64–110. https://doi.org/10.1017/etds.2013.43 |
| 2010b04 | Clay, M.; Leininger, C. J.; Mangahas, J. | The geometry of right-angled Artin subgroups of mapping class groups | 1007.1129 | Groups Geom. Dyn. 6(2) (2012), 249–278. https://doi.org/10.4171/GGD/157 |
| 2010b05 | Hubert, P.; Schmidt, T. A. | Diophantine approximation on Veech surfaces | 1010.3475 | Bull. Soc. Math. France. 140(4) (2012), 551–568. https://doi.org/10.24033/bsmf.2636 |
| 2010b06 | Kim, I.; Pansu, P. | Density of Zariski density for surface groups | 1009.2258 | Duke Math. J. 163(9) (2014), 1737–1794. https://doi.org/10.1215/00127094-2690696 |
| 2010b07 | Kim, I.; Pansu, P. | Flexibility of surface groups in classical simple Lie groups | 1101.1159 | J. Eur. Math. Soc. 17(9) (2015), 2209–2242. https://doi.org/10.4171/JEMS/555 |
| 2010b08 | Krushkal, S. | The Grunsky operator, Ahlfors question and geometry of Universal Teichmüller space | ||
| 2010b09 | Ohshika, K. | Divergence, exotic convergence and self-bumping in quasi-Fuchsian spaces | 1010.0070 | Ann. Fac. Sci. Toulouse Math. 29(4) (2020), 805–895. https://doi.org/10.5802/afst.1647 |
| 2010b10 | Kokotov, A. | Polyhedral surfaces and determinant of Laplacian | - | Proc. Amer. Math. Soc.141(2) (2013), 725–735. https://doi.org/10.1090/S0002-9939-2012-11531-X |
| 2010b11 | Hillairet, L.; Kokotov, A. | Krein formula and S-matrix for euclidean surfaces with conical singularities | 1011.5034 | J. Geom. Anal. 23(3) (2013), 1498–1529. https://doi.org/10.1007/s12220-012-9295-3 |
| 2010b12 | Athreya, J. S.; Chaika, J. | The distribution of gaps for saddle connection directions | 1012.4298 | Geom. Funct. Anal. 22(6) (2012), 1491–1516. https://doi.org/10.1007/s00039-012-0164-9 |
| 2010b13 | Delecroix, V. | Cardinality of Rauzy classes | 1106.0807 | Ann. Inst. Fourier. 63(5) (2013), 1651–1715. https://doi.org/10.5802/aif.2811 |
| 2010b14 | Forni, G.; Matheus, C.; Zorich, A. | Square-tiled cyclic covers | 1007.4275 | J. Mod. Dyn. 5(2) (2011), 285–318. https://doi.org/10.3934/jmd.2011.5.285 |
| 2010b15 | Matheus, C. | Appendix "Other relevant examples" to Giovanni Forni's paper "A geometric criterion for the nonuniform hyperbolicity of the Kontsevich-Zorich cocycle" | 1009.4655 | J. Mod. Dyn. 5(2) (2011), 355–395. https://doi.org/10.3934/jmd.2011.5.355 |
| 2010b16 | Delecroix, V.; Matheus, C. | Un contre-exemple à la réciproque du critère de Forni pour la positivité des exposants de Lyapunov du cocycle de Kontsevich-Zorich | 1103.1560 | Math. Res. Lett. 22(6) (2015), 1667–1678. https://doi.org/10.4310/MRL.2015.v22.n6.a6 |
| 2010b17 | Matheus, C.; Weitze-Schmithüsen, G. | Explicit Teichmüller curves with complemetary series | 1109.0517 | Bull. Soc. Math. France. 141(4) (2013), 557–602. https://doi.org/10.24033/bsmf.2656 |
| 2010b18 | Forni, G.; Matheus, C.; Zorich, A. | Lyapunov spectrum of invariant subbundles of the Hodge bundle | 1112.0370 | Ergodic Theory Dynam. Systems. 34(2) (2014), 353–408. https://doi.org/10.1017/etds.2012.148 |
| 2010b19 | Alessandrini, D.; Liu, L.; Papadopoulos, A.; Su, W. | The behaviour of Fenchel-Nielsen distance under a change of pants decomposition | 1105.0202 | Comm. Anal. Geom. 20(2) (2012), 369–394. https://doi.org/10.4310/CAG.2012.v20.n2.a6 |
| 2010b20 | McMullen, C. T. | Entropy on Riemann surfaces and the Jacobians of finite covers | Comment. Math. Helv. 88(4) (2013), 953–964. https://doi.org/10.4171/CMH/308 |
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| 2010b21 | McMullen, C. T. | Diophantine and ergodic foliations on surfaces | J. Topol. 6(2) (2013), 349–360. https://doi.org/10.1112/jtopol/jts033 |
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| 2010b22 | McMullen, C. T. | Navigating moduli space with complex twists | J. Eur. Math. Soc. 15(4) (2013), 1223–1243. https://doi.org/10.4171/JEMS/390 |
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| 2010b23 | Chen, D.; Möller, M. | Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus | 1104.3932 | Geom. Topol. 16(4) (2012), 2427–2479. https://doi.org/10.2140/gt.2012.16.2427 |
| 2010b24 | Eskin, A.; Kontsevich, M.; Zorich, A. | Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow | 1112.5872 | Publ. Math. Inst. Hautes Études Sci. 120 (2014), 207–333. https://doi.org/10.1007/s10240-013-0060-3 |
| 2010b25 | Eskin, A.; Kontsevich, M.; Zorich, A. | Lyapunov spectrum of square-tiled cyclic covers | 1007.5330 | J. Mod. Dyn. 5(2) (2011), 319–353. https://doi.org/10.3934/jmd.2011.5.319 |
| 2010b26 | Eskin, A.; Mirzakhani, M. | Counting closed geodesics in moduli space | 0811.2362 | J. Mod. Dyn. 5(1) (2011), 71–105. https://doi.org/10.3934/jmd.2011.5.71 |
| 2010b27 | Bowman, J. P.; Valdez, F. | Wild singularities of flat surfaces | 1110.1350 | Israel J. Math. 197(1) (2013), 69–97. https://doi.org/10.1007/s11856-013-0022-y |
| 2010b28 | Valdez, F.; Weitze-Schmithüsen, G. | On the geometry and arithmetic of infinite translation surfaces | 1102.0974 | J. Singul. 9 (2014), 226–244. https://doi.org/10.5427/jsing.2014.9r |
| 2010b29 | Bainbridge, M.; Möller, M. | The locus of real multiplication and the Schottky locus | 1107.3832 | J. Reine Angew. Math. 686 (2014), 167–186. https://doi.org/10.1515/crelle-2012-0019 |
| 2010b30 | Earle, C. J.; Marden, A. | Holomorphic plumbing coordinates | - | Contemp. Math., 575 https://doi.org/10.1090/conm/575/11411 |
| 2010b31 | Lanneau, E.; Nguyen, D-M. | Teichmüller curves generated by Weierstrass Prym eigenforms in genus 3 and genus 4 | 1111.2299 | J. Topol. 7(2) (2014), 475–522. https://doi.org/10.1112/jtopol/jtt036 |
| 2010b32 | Lenzhen, A.; Rafi, K.; Tao, J. | Bounded combinatorics and the Lipschitz metric on Teichmüller space | 1011.6078 | Geom. Dedicata. 159 (2012), 353–371. https://doi.org/10.1007/s10711-011-9664-2 |
| 2010b33 | Forni, G.; Matheus, C.; Zorich, A. | Zero Lyapunov exponents of the Hodge bundle | 1201.6075 | Comment. Math. Helv. 89(2) (2014), 489–535. https://doi.org/10.4171/CMH/325 |
| 2010b34 | Boissy, C.; Lanneau, E. | Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy | 1005.4148 | Geom. Funct. Anal. 22(1) (2012), 74–106. https://doi.org/10.1007/s00039-012-0152-0 |
| 2010b35 | Lanneau, E.; Thiffeault, J-L. | On the minimum dilatation of braids on punctured discs | 1004.5344 | Geom. Dedicata. 152 (2011), 165–182. https://doi.org/10.1007/s10711-010-9551-2 |
| 2010b36 | Marden, A. | Outer circles | - | Cambridge University Press, Cambridge, 2007. xviii+427 pp. https://doi.org/10.1017/CBO9780511618918 |
| 2010b37 | Kraaikamp, C.; Schmidt, T. A.; Steiner, W. | Natural extensions and entropy of α-continued fractions | 1011.4283 | Nonlinearity. 25(8) (2012), 2207–2243. https://doi.org/10.1088/0951-7715/25/8/2207 |
| 2010b38 | Calta, K.; Schmidt, T. A. | Continued fractions for a class of triangle groups | 1103.2076 | J. Aust. Math. Soc. 93(1-2) (2012), 21–42. https://doi.org/10.1017/S1446788712000651 |
| 2010b39 | Hubert, P.; Schmithüsen, G. | Infinite translation surfaces with infinitely generated Veech groups | - | J. Mod. Dyn. 4(4) (2010), 715–732. https://doi.org/10.3934/jmd.2010.4.715 |
| 2010b40 | Schmoll, M. | Veech groups for holonomy-free torus covers | - | J. Topol. Anal. 3(4) (2011), 521–554. https://doi.org/10.1142/S1793525311000647 |
| 2010b41 | Athreya, J. S.; Eskin, A.; Zorich, A. | Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP1 | 1212.1660 | Ann. Sci. Éc. Norm. Supér. 49(6) (2016), 1311–1386. https://doi.org/10.24033/asens.2310 |
Name |
Affiliation |
| Jayadev Athreya | Yale University |
| Artur Avila | CNRS: Université Paris Diderot-Paris 7 |
| Matthew Bainbridge | University of Aarhus |
| Ara Basmajian | City University of New York |
| Corentin Boissy | Université d'Aix-Marseille III |
| Brian H. Bowditch | University of Warwick |
| Joshua P. Bowman | Stony Brook University |
| Alexander I. Bufetov | Rice University |
| Kariane Calta | Vassar College |
| Jon Chaika | Rice University |
| Dawei Chen | University of Illinois Chicago |
| Hyomin Choi | University of Chicago |
| Aliakbar Daemi | Harvard University |
| Vincent Delecroix | Institut de Mathématiques de Luminy |
| Moon Duchin | University of Michigan |
| Alex Eskin | University of Chicago |
| Simion Filip | Cambridge University |
| Vaibhav Gadre | Harvard University |
| Ilya Gekhtman | University of Chicago |
| Ren Guo | University of Minnesota |
| Ursula Hamenstädt | Universität Bonn |
| Eriko Hironaka | Florida State University |
| W. Patrick Hooper | City College of New York |
| Pascal Hubert | Université de Provence |
| Pradthana Jaipong | University of Illinois at Urbana-Champaign |
| Chris Johnson | Clemson University |
| Christopher Judge | Indiana University |
| Inkang Kim | Korea Institute for Advanced Study |
| Dmitry Kleinbock | Brandeis University |
| Thomas Koberda | Harvard University |
| Alexey Kokotov | Concordia University |
| Yohei Komori | Osaka City University |
| Dmitry Korotkin | Concordia University |
| Samuel Krushkal | Bar-Ilan University |
| Erwan Lanneau | Université du Sud-Toulon Var |
| Christopher J. Leininger | University of Illinois at Urbana-Champaign |
| Samuel Lelievre | Université Paris-Sud 11 |
| Anna Lenzhen | Université de Rennes 1 |
| Lixin Liu | Zongshan (Sun Yat-Sen) University |
| José Ferrán Valdez Lorenzo | UNAM |
| Joseph Maher | CUNY College of Staten Island |
| Sara Maloni | University of Warwick |
| Johanna Mangahas | University of Michigan |
| Luca Marchese | Université de Geneve |
| Albert Marden | University of Minnesota |
| Gaven John Martin | Massey University |
| Howard Masur | University of Chicago |
| Gabriele Mondello | Università di Roma "La Sapienza" |
| Thierry Monteil | LIRMM-CNRS (UMR 5506) |
| Martin Möller | Goethe-Universität Frankfurt |
| Ken'ichi Ohshika | Osaka University |
| Suhas Jaykumar Pandit | Indian Institute of Science Education and Research |
| Athanase Papadopoulos | University of Strasbourg |
| Kasra Rafi | University of Oklahoma |
| Carlos Matheus Silva Santos | College de France |
| Thomas Schmidt | Oregon State University |
| Gabriela Schmithuesen | Karlsruhe Institute of Technology (KIT) |
| Martin J. Schmoll | Clemson University |
| Aaron Silberstein | Harvard University |
| John Smillie | Cornell University |
| Weixu Su | Sun Yat-Sen University |
| Jing Tao | University of Utah |
| Giulio Tiozzo | Harvard University |
| Corinna Ulcigrai | University of Bristol |
| Karen Vogtmann | Cornell University |
| Barak Weiss | Ben-Gurion University |
| Alexander Wright | University of Chicago |
| Jean-Christophe Yoccoz | Collège de France |
| Anton Zorich | Université de Rennes 1 |
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