Universität Bonn

Trimester Program: "Geometry and Dynamics of Teichmüller Spaces"

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

Publications

No. Author(s) Title Preprint Publication
2010b01 Bugeaud, Y.; Hubert, P.; Schmidt, T. A. Transcendence with Rosen continued fractions 1007.20504 J. Eur. Math. Soc. 15(1) (2013), 39–51.
https://doi.org/10.4171/JEMS/3555
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/jtt0056
2010b03 Calegari, D.; Maher, J. Statistics and compression of scl 1008.49527 Ergodic Theory Dynam. Systems. 35(1) (2015), 64–110.
https://doi.org/10.1017/etds.2013.438
2010b04 Clay, M.; Leininger, C. J.; Mangahas, J. The geometry of right-angled Artin subgroups of mapping class groups 1007.11299 Groups Geom. Dyn. 6(2) (2012), 249–278.
https://doi.org/10.4171/GGD/15710
2010b05 Hubert, P.; Schmidt, T. A. Diophantine approximation on Veech surfaces 1010.347511 Bull. Soc. Math. France. 140(4) (2012), 551–568.
https://doi.org/10.24033/bsmf.263612
2010b06 Kim, I.; Pansu, P. Density of Zariski density for surface groups 1009.225813 Duke Math. J. 163(9) (2014), 1737–1794.
https://doi.org/10.1215/00127094-269069614
2010b07 Kim, I.; Pansu, P. Flexibility of surface groups in classical simple Lie groups 1101.115915 J. Eur. Math. Soc. 17(9) (2015), 2209–2242.
https://doi.org/10.4171/JEMS/55516
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 1010.007017 Ann. Fac. Sci. Toulouse Math. 29(4) (2020), 805–895.
https://doi.org/10.5802/afst.164718
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-X19
2010b11 Hillairet, L.; Kokotov, A. Krein formula and S-matrix for euclidean surfaces with conical singularities 1011.503420 J. Geom. Anal. 23(3) (2013), 1498–1529.
https://doi.org/10.1007/s12220-012-9295-321
2010b12 Athreya, J. S.; Chaika, J. The distribution of gaps for saddle connection directions 1012.429822 Geom. Funct. Anal. 22(6) (2012), 1491–1516.
https://doi.org/10.1007/s00039-012-0164-923
2010b13 Delecroix, V. Cardinality of Rauzy classes 1106.080724 Ann. Inst. Fourier. 63(5) (2013), 1651–1715.
https://doi.org/10.5802/aif.281125
2010b14 Forni, G.; Matheus, C.; Zorich, A. Square-tiled cyclic covers 1007.427526 J. Mod. Dyn. 5(2) (2011), 285–318.
https://doi.org/10.3934/jmd.2011.5.28527
2010b15 Matheus, C. Appendix "Other relevant examples" to Giovanni Forni's paper "A geometric criterion for the nonuniform hyperbolicity of the Kontsevich-Zorich cocycle" 1009.465528 J. Mod. Dyn. 5(2) (2011), 355–395.
https://doi.org/10.3934/jmd.2011.5.35529
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 1103.156030 Math. Res. Lett. 22(6) (2015), 1667–1678.
https://doi.org/10.4310/MRL.2015.v22.n6.a631
2010b17 Matheus, C.; Weitze-Schmithüsen, G. Explicit Teichmüller curves with complemetary series 1109.051732 Bull. Soc. Math. France. 141(4) (2013), 557–602.
https://doi.org/10.24033/bsmf.265633
2010b18 Forni, G.; Matheus, C.; Zorich, A. Lyapunov spectrum of invariant subbundles of the Hodge bundle 1112.037034 Ergodic Theory Dynam. Systems. 34(2) (2014), 353–408.
https://doi.org/10.1017/etds.2012.14835
2010b19 Alessandrini, D.; Liu, L.; Papadopoulos, A.; Su, W. The behaviour of Fenchel-Nielsen distance under a change of pants decomposition 1105.020236 Comm. Anal. Geom. 20(2) (2012), 369–394.
https://doi.org/10.4310/CAG.2012.v20.n2.a637
2010b20 McMullen, C. T. Entropy on Riemann surfaces and the Jacobians of finite covers pdf38 Comment. Math. Helv. 88(4) (2013), 953–964.
https://doi.org/10.4171/CMH/30839
2010b21 McMullen, C. T. Diophantine and ergodic foliations on surfaces pdf40 J. Topol. 6(2) (2013), 349–360.
https://doi.org/10.1112/jtopol/jts03341
2010b22 McMullen, C. T. Navigating moduli space with complex twists pdf42 J. Eur. Math. Soc. 15(4) (2013), 1223–1243.
https://doi.org/10.4171/JEMS/39043
2010b23 Chen, D.; Möller, M. Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus 1104.393244 Geom. Topol. 16(4) (2012), 2427–2479.
https://doi.org/10.2140/gt.2012.16.242745
2010b24 Eskin, A.; Kontsevich, M.; Zorich, A. Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow 1112.587246 Publ. Math. Inst. Hautes Études Sci. 120 (2014), 207–333.
https://doi.org/10.1007/s10240-013-0060-347
2010b25 Eskin, A.; Kontsevich, M.; Zorich, A. Lyapunov spectrum of square-tiled cyclic covers 1007.533048 J. Mod. Dyn. 5(2) (2011), 319–353.
https://doi.org/10.3934/jmd.2011.5.31949
2010b26 Eskin, A.; Mirzakhani, M. Counting closed geodesics in moduli space 0811.236250 J. Mod. Dyn. 5(1) (2011), 71–105.
https://doi.org/10.3934/jmd.2011.5.7151
2010b27 Bowman, J. P.; Valdez, F. Wild singularities of flat surfaces 1110.135052 Israel J. Math. 197(1) (2013), 69–97.
https://doi.org/10.1007/s11856-013-0022-y53
2010b28 Valdez, F.; Weitze-Schmithüsen, G. On the geometry and arithmetic of infinite translation surfaces 1102.097454 J. Singul. 9 (2014), 226–244.
https://doi.org/10.5427/jsing.2014.9r55
2010b29 Bainbridge, M.; Möller, M. The locus of real multiplication and the Schottky locus 1107.383256 J. Reine Angew. Math. 686 (2014), 167–186.
https://doi.org/10.1515/crelle-2012-001957
2010b30 Earle, C. J.; Marden, A. Holomorphic plumbing coordinates - Contemp. Math., 575
https://doi.org/10.1090/conm/575/1141158
2010b31 Lanneau, E.; Nguyen, D-M. Teichmüller curves generated by Weierstrass Prym eigenforms in genus 3 and genus 4 1111.229959 J. Topol. 7(2) (2014), 475–522.
https://doi.org/10.1112/jtopol/jtt03660
2010b32 Lenzhen, A.; Rafi, K.; Tao, J. Bounded combinatorics and the Lipschitz metric on Teichmüller space 1011.607861 Geom. Dedicata. 159 (2012), 353–371.
https://doi.org/10.1007/s10711-011-9664-262
2010b33 Forni, G.; Matheus, C.; Zorich, A. Zero Lyapunov exponents of the Hodge bundle 1201.607563 Comment. Math. Helv. 89(2) (2014), 489–535.
https://doi.org/10.4171/CMH/32564
2010b34 Boissy, C.; Lanneau, E. Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy 1005.414865 Geom. Funct. Anal. 22(1) (2012), 74–106.
https://doi.org/10.1007/s00039-012-0152-066
2010b35 Lanneau, E.; Thiffeault, J-L. On the minimum dilatation of braids on punctured discs 1004.534467 Geom. Dedicata. 152 (2011), 165–182.
https://doi.org/10.1007/s10711-010-9551-268
2010b36 Marden, A. Outer circles - Cambridge University Press, Cambridge, 2007. xviii+427 pp.
https://doi.org/10.1017/CBO978051161891869
2010b37 Kraaikamp, C.; Schmidt, T. A.; Steiner, W. Natural extensions and entropy of α-continued fractions 1011.428370 Nonlinearity. 25(8) (2012), 2207–2243.
https://doi.org/10.1088/0951-7715/25/8/220771
2010b38 Calta, K.; Schmidt, T. A. Continued fractions for a class of triangle groups 1103.207672 J. Aust. Math. Soc. 93(1-2) (2012), 21–42.
https://doi.org/10.1017/S144678871200065173
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.2010.4.71574
2010b40 Schmoll, M. Veech groups for holonomy-free torus covers - J. Topol. Anal. 3(4) (2011), 521–554.
https://doi.org/10.1142/S179352531100064775
2010b41 Athreya, J. S.; Eskin, A.; Zorich, A. Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP1 1212.166076 Ann. Sci. Éc. Norm. Supér. 49(6) (2016), 1311–1386.
https://doi.org/10.24033/asens.231077

Participants

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
Poster TP_2010_05.jpg
© HIM

Links

  1. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2010_05#pubs
  2. https://www.mathematics.uni-bonn.de/en/programs/assets/report-tp_2010_05.pdf
  3. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2010_05#part
  4. http://arxiv.org/abs/1007.2050
  5. https://doi.org/10.4171/JEMS/355
  6. https://doi.org/10.1112/jtopol/jtt005
  7. http://arxiv.org/abs/1008.4952
  8. https://doi.org/10.1017/etds.2013.43
  9. http://arxiv.org/abs/1007.1129
  10. https://doi.org/10.4171/GGD/157
  11. http://arxiv.org/abs/1010.3475
  12. https://doi.org/10.24033/bsmf.2636
  13. http://arxiv.org/abs/1009.2258
  14. https://doi.org/10.1215/00127094-2690696
  15. http://arxiv.org/abs/1101.1159
  16. https://doi.org/10.4171/JEMS/555
  17. http://arxiv.org/abs/1010.0070
  18. https://doi.org/10.5802/afst.1647
  19. https://doi.org/10.1090/S0002-9939-2012-11531-X
  20. http://arxiv.org/abs/1011.5034
  21. https://doi.org/10.1007/s12220-012-9295-3
  22. http://arxiv.org/abs/1012.4298
  23. https://doi.org/10.1007/s00039-012-0164-9
  24. http://arxiv.org/abs/1106.0807
  25. https://doi.org/10.5802/aif.2811
  26. http://arxiv.org/abs/1007.4275
  27. https://doi.org/10.3934/jmd.2011.5.285
  28. http://arxiv.org/abs/1009.4655
  29. https://doi.org/10.3934/jmd.2011.5.355
  30. http://arxiv.org/abs/1103.1560
  31. https://doi.org/10.4310/MRL.2015.v22.n6.a6
  32. http://arxiv.org/abs/1109.0517
  33. https://doi.org/10.24033/bsmf.2656
  34. http://arxiv.org/abs/1112.0370
  35. https://doi.org/10.1017/etds.2012.148
  36. http://arxiv.org/abs/1105.0202
  37. https://doi.org/10.4310/CAG.2012.v20.n2.a6
  38. http://math.harvard.edu/~ctm/papers/home/text/papers/covs/covs.pdf
  39. https://doi.org/10.4171/CMH/308
  40. http://math.harvard.edu/~ctm/papers/home/text/papers/dioph/dioph.pdf
  41. https://doi.org/10.1112/jtopol/jts033
  42. http://math.harvard.edu/~ctm/papers/home/text/papers/nav/nav.pdf
  43. https://doi.org/10.4171/JEMS/390
  44. http://arxiv.org/abs/1104.3932
  45. https://doi.org/10.2140/gt.2012.16.2427
  46. http://arxiv.org/abs/1112.5872
  47. https://doi.org/10.1007/s10240-013-0060-3
  48. http://arxiv.org/abs/1007.5330
  49. https://doi.org/10.3934/jmd.2011.5.319
  50. http://arxiv.org/abs/0811.2362
  51. https://doi.org/10.3934/jmd.2011.5.71
  52. http://arxiv.org/abs/1110.1350
  53. https://doi.org/10.1007/s11856-013-0022-y
  54. http://arxiv.org/abs/1102.0974
  55. https://doi.org/10.5427/jsing.2014.9r
  56. http://arxiv.org/abs/1107.3832
  57. https://doi.org/10.1515/crelle-2012-0019
  58. https://doi.org/10.1090/conm/575/11411
  59. http://arxiv.org/abs/1111.2299
  60. https://doi.org/10.1112/jtopol/jtt036
  61. http://arxiv.org/abs/1011.6078
  62. https://doi.org/10.1007/s10711-011-9664-2
  63. http://arxiv.org/abs/1201.6075
  64. https://doi.org/10.4171/CMH/325
  65. http://arxiv.org/abs/1005.4148
  66. https://doi.org/10.1007/s00039-012-0152-0
  67. http://arxiv.org/abs/1004.5344
  68. https://doi.org/10.1007/s10711-010-9551-2
  69. https://doi.org/10.1017/CBO9780511618918
  70. http://arxiv.org/abs/1011.4283
  71. https://doi.org/10.1088/0951-7715/25/8/2207
  72. http://arxiv.org/abs/1103.2076
  73. https://doi.org/10.1017/S1446788712000651
  74. https://doi.org/10.3934/jmd.2010.4.715
  75. https://doi.org/10.1142/S1793525311000647
  76. http://arxiv.org/abs/1212.1660
  77. https://doi.org/10.24033/asens.2310
  78. https://www.mathematics.uni-bonn.de/him/programs/past/tp_2010_05#start