Wintersemester 2018/19:

Lehre vergangener Semester:

• SoSe 19: Komplexe Algebraische Geometrie II
• WiSe 18/19: Komplexe Algebraische Geometrie

Research Interests:

• Moduli space of curves: Teichmüller curves, flat surfaces, Teichmüller dynamics
• Abelian varieties: Shimura varieties, Hilbert modular surfaces, theta functions
• Fuchsian groups: triangle groups, quadrilateral groups, arithmetic Fuchsian groups
• Belyi-Grothendieck theory: dessins d'enfants, Beauville surfaces

Publications:

• Euler characteristics of Gothic Teichmüller curves (with M. Möller) [arXiv], Geom. Topol., to appear (2019).
• Orbifold points on Prym-Teichmüller curves on genus four (with J. Zachhuber) [arXiv, journal], J. Inst. Math. Jussieu, Vol. 18 (2019), Issue 4, 673-706.
  PARI/GP code: [files, documentation]
• Arbitrarily large Galois orbits of non-homeomorphic surfaces (with G. González-Diez and G. A. Jones) [arXiv, journal], European Journal of Mathematics 4 (2018), Issue 1, 223-241.
• Orbifold points on Prym-Teichmüller curves on genus three (with J. Zachhuber) [arXiv, journal], Int. Math. Res. Notices, Vol. 2018, Issue 4, 1228-1280.
  PARI/GP code: [files, documentation]
• Fields of definition of uniform dessins on quasiplatonic surfaces (with E. Girondo and J. Wolfart), [pdf, journal, Appendix], in Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces, Contemporary Mathematics, 629 (2014), 155-170.
• Beauville surfaces with abelian Beauville group (with G. González-Diez and G. A. Jones) [arXiv, journal], Math. Scand. 114 (2014), no. 2, 191-204.
• Non-homeomorphic Galois conjugate Beauville structures on PSL(2,p) (with G. González-Diez) [pdf, journal], Adv. Math. 229 (2012), no. 6, 3096–3122.
• Shimura curves with many uniform dessins (with E. Girondo and J. Wolfart) [pdf, journal], Math. Z. 271 (2012), no. 3-4, 757-779.
• An introduction to Beauville surfaces via uniformization (with G. González-Diez) [pdf, journal], in Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces, Contemporary Mathematics, 575 (2012), 123-151.
• Genus 2 Belyi surfaces with a unicellular uniform dessin (with E. Girondo) [pdf, journal], Geom. Dedicata 155 (2011), 81-103.
• Z_N-curves Possessing No Thomae Formulae of Bershadsky–Radul Type (with G. González-Diez) [pdf, journal], Lett. Math. Phys. 98 (2011), no. 2, 193-205.

Preprints:

• Masur-Veech volume of the gothic locus [arXiv] (2019).

Others:

• Triangle groups, dessins d'enfants and Beauville surfaces [pdf], PhD thesis (2012).
• Álgebras de cuaterniones y grupos fuchsianos aritméticos [pdf], master's course taught in Chile, 2012 (summary in Spanish).