Prof. Dr. Martin Möller

Forschungssemester im SoSe 2024

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

(53) Spectral decomposition and Siegel-Veech transforms for strata: The case of marked tori (with Jayadev Athreya, Jean Lagacé, Martin Raum)
arXiv: 2404.06597
Latest version (pdf)

(52) A smooth compactification of spaces of stability conditions: the case of the An-quiver (with Anna Barbieri and Jeonghoon So) 
arXiv: 2312.02686
Latest Version (pdf)

(51) Teichmüller curves in hyperelliptic components of meromorphic strata (with Scott Mullane)
arXiv: 2305.03309
Latest Version (pdf)

(50) Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients (with Matteo Costantini and Johannes Schwab)
arXiv: 2303.17929
Latest Version (pdf)

(49) Quadratic differentials as stability conditions: collapsing subsurfaces (with Anna Barbieri, Yu Qiu and Jeonghoon So)
arXiv: 2212.08433
Latest Version (pdf)

(48) A tale of two moduli spaces: logarithmic and multi-scale differentials (with Dawei Chen, Samuel Grushevsky, David Holmes and Johannes Schmitt)
arXiv: 2212.04704
Latest Version (pdf)

(47) On the Kodaira dimension of moduli spaces of Abelian differentials (with Dawei Chen and Matteo Costantini) (April, 2022)
arXiv: 2204.11943
Latest version (pdf)

[Download] GP/Pari files for the computer assisted proofs:
onezerostrata, onezerobruteforce

(46) Compactifying the rank two Hitchin system via spectral data on semistable curves (with Johannes Horn) (arXiv: 2201.08104)
  (to appear in Algebraic Geometry)
  Latest Version (pdf)

(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)
  (Experimental Mathematics 32 (2023), no.3, 545-565)
  Latest Version (pdf)

(44) The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials (with Matteo Costantini and Jonathan Zachhuber) (arXiv: 2006.12803)
  (Forum of Mathematics, Pi, Volume 10, 2022)
  Latest Version (pdf)

(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)
  (Duke Math. J. 172 (9), 1735-1779)
  Latest Version (pdf)

(42) The area is a good enough metric (with Matteo Costantini and Jonathan Zachhuber) (arXiv: 1910.14151)
  (to appear in Ann. Inst. Fourier)
  Latest Version (pdf)

(41) The moduli space of multi-scale differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (October, 2019)
  arXiv: 1910.13492
  Latest Version (pdf)

(40) Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials (with Dawei Chen, Adrien Sauvaget and Don Zagier)
arXiv: 1901.01785
  (Invent. Math. 222 (2020), no. 1, 283-373)
  Latest Version (pdf)

(39) Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials (with Elise Goujard) (arXiv: 1809.05016)
  (Algebr. Geom. Topol. 20 (2020), no. 5, 2451-2510)
  Latest Version (pdf)

(38) Euler characteristics of Gothic Teichmüller curves. (with David Torres-Teigell) (arXiv: 1807.10260)
  (Geom. Topol. 24 (2020), no. 3, 1149-1210)
  Latest Version (pdf)

(37) Realizability of tropical canonical divisors (with Martin Ulirsch and Annette Werner) (arXiv: 1710.06401)
  (J. Eur. Math. Soc. 23 (2021), no. 1, 185-217)
  Latest Version (pdf)

(36) Cones of Heegner divisors (with Jan Hendrik Bruinier) (arXiv: 1705.05534)
  (J. Algebraic Geom. 28 (2019), 497-517)
  Latest Version (pdf)

(35) Non-existence and finiteness results for Teichmueller curves in Prym loci (with Erwan Lanneau) (arXiv: 1704.03210)
  (Experimental Mathematics 31 (2022), no. 2, 621-636)
  Latest Version (pdf)


[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#

(34) Strata of k-differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (arXiv: 1610.09238)
  (Algebr. Geom. 6 (2019), no. 2, 196–233)
  Latest Version (pdf)

(33) Counting Feynman-like graphs: Quasimodularity and Siegel-Veech weight (with Elise Goujard) (arXiv: 1609.01658)
  (J. Europ. Math. Soc. 22 (2020), 365-412)
  Latest Version (pdf)

(32) Lower bounds for Lyapunov exponents of flat bundles on curves (with Alex Eskin, Maxim Kontsevich and Anton Zorich) (arXiv: 1609.01170)
  (Geom. Topol. 22 (2018), no. 4, 2299–2338)
  Latest Version (pdf)

(31) Quasimodularity and large genus limits of Siegel-Veech constants (with Dawei Chen and Don Zagier) (arXiv:1606.04065)
  (J. Amer. Math. Soc. 31 (2018), no. 4, 1059–1163)
  Latest Version (pdf)

(30) Compactification of strata of abelian differentials (with Matt Bainbridge, Dawei Chen, Quentin Gendron and Samuel Grushevsky) (arXiv:1604.08834)
  (Duke Math. J. 167 (2018), no. 12, 2347–2416)
  Latest Version (pdf)

(29) Explicit formulas for infinitely many Shimura curves in genus 4 (with Samuel Grushevsky) (arXiv:1510_05674)
  (Asian J. Math. 22 (2018), no. 2, 381–390)
  Latest Version (ps) Latest Version (pdf)

(28) Cutting out arithmetic Teichmüller curves in genus two via Theta functions (with André Kappes) (arXiv:1504.00470)
  (Comment. Math. Helv.  92  (2017), 257–309)
  Latest Version (pdf)

(27) Modular embeddings of Teichmüller curves (with Don Zagier) (arXiv:1503.05690)
  (Compositio Math. 152 (2016), 2269-2349)
  Latest Version (ps) Latest Version (pdf)

(26) Teichmüller curves in genus three and just likely intersections in Gnm × Gna (with Matt Bainbridge and Philipp Habegger) (arXiv:1410.6835)
  (Publ. Math. IHES, Vol. 124 No. 1 (2016), 1-98)
  Latest Version (pdf)

  [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)
  (Algebra and Number Theory 9-4 (2015), 897-912)
  Latest Version (pdf)

(24) Shimura curves within the locus of genus3 hyperelliptic curves (with Samuel Grushevsky) (arXiv:1308.5155)
  (Int Math Res Notices (2016) Vol. 2016 1603-1639)
  Latest Version (ps) Latest Version (pdf)

(23) A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (with Carlos Matheus and Jean-Christophe Yoccoz) (arXiv:1305.2033)
  (Invent. Math. 202 (2013), 333-425)
  Latest Version (pdf)

(22) Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle (with Artur Avila and Alex Eskin) (arXiv:1209.2854)
  (J. Reine Angew. Math. 732 (2017), 1–20)
  Latest Version (ps) Latest Version (pdf)

(21) Lyapunov spectrum of ball quotients with applications to commensurability questions (with Andre Kappes) (arXiv:1207.5433)
  (Duke Math. Journal, 165 (2016), 1-66)
  Latest Version (ps) Latest Version (pdf)

(20) Quadratic differentials in low genus: exceptional and non-varying (with Dawei Chen) (arXiv:1204.1707)
  (Ann. Sci. ENS 47 (2014), 309–370)
  Latest Version (ps) Latest Version (pdf)

(19) Prym covers, theta functions and Kobayashi geodesics in Hilbert modular surfaces
  (Amer. Journal. of Math. 136 (2014), 995–1022)
  Latest Version (ps) Latest Version (pdf)

(18) The locus of real multiplication and the Schottky locus (with Matt Bainbridge) (arXiv:1107.3832)
  (J. Reine Angew. Math. 685 (2014), 167-186)
  Latest Version (ps) Latest Version (pdf)

(17) Non-varying sums of Lyapunov exponents of Abelian differentials in low genus (with Dawei Chen) (arXiv: 1104.3932)
  (Geometry and Topology 12 (2012), 101-154)
  Latest Version (ps) Latest Version (pdf)

(16) Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant (with A. Pohl) ( math.DS/1103.5235)
  (Erg.Th.Dyn.Syst. 33 (2013), 247-283)
  Latest Version (ps) Latest Version (pdf)

(15) The Deligne-Mumford-compactification of Hilbert modular varieties and Teichmueller curves in genus three (with Matt Bainbridge) (math.AG/0911.4677)
  (Acta Math. 208  (2012), 1-92)
  Latest Version (ps) Latest Version (pdf)

(14) Kobayashi geodesics in A_g (with Eckart Viehweg) (math.AG/0809.1018)
  (Journal of Diff. Geom 86 Nr. 2 (2011), 355--379)
  Latest Version (ps) Latest Version (pdf)

(13) Differential equations associated with nonarithmetic Fuchsian groups (with Irene Bouw) ( math.AG/0710.5277)
  (Journal London Math. Soc. 81 No. 1 (2010), 65-90)
  Latest Version (ps) Latest Version (pdf)

(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. Ann 353 (2012), 1-35)
  Latest Version (ps) Latest Version (pdf)

(11) Stability of Hodge bundles and a numerical characterization of Shimura varieties (with Eckart Viehweg and Kang Zuo) (Mathematics arXiv: math.AG/0706.3462)
  (Journ. Diff. Geom. 92 (2012), 71-151)
  Latest Version (ps) Latest Version (pdf)

(10) Linear manifolds in the moduli space of one-forms (math.AG/0703145)
  (Duke Math. J. 144 No.3 (2008), 447-488)
  Latest Version (ps) Latest Version (pdf)

(9) The Arnoux-Yoccoz Teichmüller disc (with Pascal Hubert and Erwan Lanneau) (math.AG/0611655)
  (GAFA 18 No. 6 (2008), 1988-2016)
  Latest Version (ps) Latest Version (pdf)

(8) Teichmüller curves, triangle groups, and Lyapunov exponents (with Irene Bouw) (math.AG/0511738)
  (Annals of Math. 172 (2010), 139-185)
  Latest Version (ps) Latest Version (pdf) (math.AG/0509079)

(7) Finiteness results for Teichmueller curves
  (Ann. Inst. Fourier 58 (2008), 63-83)
  Latest Version (ps) Latest Version (pdf)

(6) Shimura- and Teichmueller curves  (math.AG/0501333)
  (Journal Modern Dynamics 5 No.1 (2011),1-32)
  Latest Version (ps) Latest Version (pdf)

(5) Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmueller curve (math.AG/0410262)
  (Invent. Math. 165 No. 3 (2006), 633-649)
  Latest Version (ps) Latest Version (pdf)

(4) Variations of Hodge structure of Teichmueller curves (math.AG/0401290)
  (Journal of the AMS 19 (2006), 327-344)
  Latest Version (ps) Latest Version (pdf)

(3) Teichmueller curves, Galois actions and GT-relations (math.AG/0311308)
  (Math. Nachrichten 278 No. 9 (2005),1061–1077)
  Latest Version (ps) Latest Version (pdf)

(2) Isotrivially fibred isles in the moduli space of surfaces of general type (math.AG/0210318)
  (Proc. AMS 133 No.2 (2005),357–362)
  Latest Version (ps) Latest Version (pdf)

(1) Maximally irregularly fibred surfaces of general type (math.AG/0209120)
  (Manusc. Math. 116 (2005),71–92)
  Latest Version (ps) Latest Version (pdf)

TU Darmstadt, GU Frankfurt, Univ. Heidelberg

TU Darmstadt und GU Frankfurt  (01/18 - 12/22)

(10/10 - 09/15)

WiSe 23/24
SoSe 23
WiSe 22/23
SoSe 22
WiSe 21/22
SoSe 21 F O R S C H U N G S S E M E S T E R
  • Forschungsseminar DaFraHeiMai/GAUS-Seminar:
    The P=W conjecture  [Programm]
  • Oberseminar Algebra und Geometrie
  • BISTRO-Seminar
    (Billiards, surfaces à la Teichmüller and Riemann, Online)
    organized by Simion Filip, Carlos Matheus, Curtis McMullen and Martin Möller
WiSe 20/21
SoSe 2020
WiSe 19/20 F O R S C H U N G S S E M E S T E R

SoSe 19

WiSe 18/19

SoSe 18

WiSe 17/18

SoSe 17

WiSe 16/17
SoSe 16 F O R S C H U N G S S E M E S T E R
  • Oberseminar Algebra und Geometrie
  • Forschungs- und Oberseminar: arXiv-Seminar (Programm)
WiSe 15/16   
SoSe 15 F O R S C H U N G S S E M E S T E R
WiSe 14/15
SoSe 14 F O R S C H U N G S S E M E S T E R
WiSe 13/14
SoSe 13
WiSe 12/13
SoSe 12 F O R S C H U N G S S E M E S T E R

WiSe 11/12
SoSe 11
WiSe 10/11

Skripte zu den Vorlesungen



Algebra        WiSe 22/23
Algebraische Geometrie   WiSe 15/16 
Darstellungstheorie   SoSe 13
Ergodentheorie   WiSe 14/15
Funktionentheorie und gewöhnliche DGL   WiSe 13/14 (aktualisiert am 6.5.2019)
Geometrie für Lehramtskandidaten
(Martin Möller / Jürgen Wolfart)
  SoSe 2020  (Version vom 17.9.2020)
Kommutative Algebra   SoSe 18
Lineare Algebra I   WiSe 21/22
Lineare Algebra II SoSe 22
Lineare Algebra für Sekundarstufe I (L2/L5)
(Martin Möller / Jürgen Wolfart)
  SoSe 18
Modulformen   SoSe 17
Riemannsche Flächen   WiSe 17/18  (aktualisiert am 3.8.2020)

Prof. Dr. Martin Möller

FB12 - Institut für Mathematik
Goethe-Universität Frankfurt  
Robert-Mayer-Str. 6-8
60325 Frankfurt am Main

Office: 218
Phone: +49 69 798 - 28945


Büro für Algebra und Geometrie:

Matthias Colmar
R.-M.-Str. 6-8, Office: 219
Phone: +49 69 798 - 22309
E-Mail: colmar[at]

Karin Nitsche
R.-M.-Str. 6-8, Office: 207
Phone: +49 69 798 - 23693
E-Mail: nitsche[at]

Fax: +49 69 798 - 22302