ERC-Starting grant: "Flat surfaces"

SL (2,R)-action on flat surfaces and geometry of extremal subvarieties of moduli spaces FP7_01

Members and associated members of the group:
(2010 - 2015)



The latest version in general contain (minor) corrections and improvements with respect to the arxiv version.

(21) Quasimodularity and large genus limits of Siegel-Veech constants
(Dawei Chen, Martin Möller and Don Zagier)
(June 2016)
  Latest Version (pdf)
(20) Explicit formulas for infinitely many Shimura curves in genus 4
(Samuel Grushevsky and Martin Möller)
(October 2015)
  Latest Version (ps) Latest Version (pdf)
(19) Cutting out arithmetic Teichmüller curves in genus two via Theta functions
(André Kappes and Martin Möller)
(April 2015)
  Latest Version (ps) Latest Version (pdf)
(18) The Deligne-Mumford and the Incidence Variety Compactifications of the Strata of the moduli space of Abelian differentials (Quentin Gendron) (March 2015)
  Latest Version (ps) Latest Version (pdf)
(17) Modular embeddings of Teichmüller curves (Martin Möller and Don Zagier)
  (to appear: in Compositio Mathematica (2016))
  Latest Version (ps) Latest Version (pdf)
(16) Orbifold points on Prym-Teichmüller curves in genus three
(David Torres-Teigell and Jonathan Zachhuber)
(February 2015)
  Latest Version (pdf)
(15) Teichmüller curves in genus three and just likely intersections in Gnm × Gna
(Matt Bainbridge, Philipp Habegger and Martin Möller)
  (to appear in: Publ. Math. IHES (2016))
  Latest Version (ps) Latest Version (pdf)
  [Download] Sage file for the computer assisted proofs: g3fin_ch6.sage and g3fin_ch9.sage
(14) Bounded negativity of self-intersection numbers of shimura curves on shimura surfaces (Martin Möller and Domingo Toledo) (arXiv:1407.5181)
  (Algebra and Number Theory 9-4 (2015), 897-912)
  Latest Version (ps) Latest Version (pdf)
(13) On the Critical Exponent of Infinitely Generated Veech Groups (Ralf Lehnert) (April 2014)
  Latest Version (pdf)
(12) Shimura curves within the locus of genus3 hyperelliptic curves (Samuel Grushevsky and Martin Möller) (arXiv:1308.5155)
  (Int Math Res Notices (2016) Vol. 2016 1603-1639)
  Latest Version (ps) Latest Version (pdf)
(11) A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (Carlos Matheus, Martin Möller and Jean-Christophe Yoccoz) (arXiv:1305.2033)
  (Invent. Math. 202 (2013), 333-425)
  Latest Version (pdf)
(10) Lyapunov Exponents of Rank 2-Variations of Hodge Structures and Modular Embeddings (André Kappes) (arXiv:1303.1088)
  (Ann. Inst. Fourier (Grenoble) (2014), 2037--2066) 
  Latest Version (ps) Latest Version (pdf)
 (9) Non-congruence of homology Veech groups in genus two (Christian Weiß) (January 2013)
  Latest Version (ps) Latest Version (pdf)
 (8) Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle (Artur Avila, Alex Eskin and Martin Möller) (arXiv:1209.2854)
  (to appear in: J. reine und angew. Math (2012))
  Latest Version (ps) Latest Version (pdf)
 (7) Twisted Teichmüller curves (Christian Weiß) (arXiv:1208.1895) 
(Lecture Notes in Mathematics, Vol. 2104 2014, xvi+166)
  Latest Version (ps) Latest Version (pdf)
 (6) Lyapunov spectrum of ball quotients with applications to commensurability questions (André Kappes and Martin Möller) (arXiv:1207.5433) 
  (Duke Math. Journal, 165 (2016), 1-66)
  Latest Version (ps) Latest Version (pdf) 
 (5) Quadratic differentials in low genus: exceptional and non-varying (Dawei Chen and Martin Möller) (arXiv:1204.1707) 
  (Ann. Sci. ENS 47 (2014), 309–370) 
  Latest Version (ps) Latest Version (pdf) 
 (4) Prym covers, theta functions and Kobayashi geodesics in Hilbert modular surfaces (Martin Möller)
  (Amer. Journal. of Math. 135 (2014), 995–1022) 
  Latest Version (ps) Latest Version (pdf)
 (3) The locus of real multiplication and the Schottky locus (Matt Bainbridge and Martin Möller) (arXiv:1107.3832) 
  (J. Reine Angew. Math. 686 (2014), 167-186) 
  Latest Version (ps) Latest Version (pdf) 
 (2) Non-varying sums of Lyapunov exponents of Abelian differentials in low genus
(Dawei Chen and Martin Möller)
(arXiv: 1104.3932) 
  (Geometry and Topology 12 (2012), 101-154) 
  Latest Version (ps) Latest Version (pdf) 
 (1) Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant
(Martin Möller and Anke Pohl)
( math.DS/1103.5235) 
  (Erg.Th.Dyn.Syst. 33 (2013), 247-283)
  Latest Version (ps) Latest Version (pdf)