Research interests
- Uniformization of Riemann surfaces
- Hyperbolic geometry
- Dessins d'Enfants
- Teichmüller Theory
- Monodromy groups of Fuchsian differential equations
- Algebraic curves
My main field of interest are compact Riemann surfaces. For me,
this is an extremely beautiful meeting point of a wide range of
subjects like complex analysis, hyperbolic geometry, algebraic
geometry, group theory, number theory, combinatorics and
theoretical physics. Just to name a few!
I am eager to collaborate with anyone interested in these
subjects. Pre-docs, post-docs, senior academics... everybody is
more than welcome to contact me.
My secondary, non-professional main scientific interest is
astronomy and astrophysics.
Publications
- A classification of extremal disc-packings in compact
non-orientable surfaces of genus three (with Cristian Reyes).
Preprint. SageMath code related to the paper will be uploaded
here soon.
- Extremal k-packings in compact non-orientable surfaces
(with Cristian Reyes). Experimental Mathematics (2022), DOI:
10.1080/10586458.2022.2075491 (published only online for the
moment).
- La teoría de Belyi-Grothendieck de dessins d'enfants
(with Gabino González-Diez and David Torres-Téigell). Gaceta de
la RSME 25, (2022), no.1 , 55-83.
- A brute force computer aided proof of an existence result
about extremal hyperbolic surfaces (with Cristian Reyes).
Contemporary Mathematics 766 (2021), 133-152.
- SageMath code for constructing a surface in the case N=14,
k=3, g=6: jupyter
file, pdf
file
- SageMath code for checking that our example for the case the
case N=14, k=3, g=6 contains a second extremal 3-packing; jupyter file,
pdf file
- SageMath code for checking that our rest of examples
contains a second extremal k-packing
- Case N=7, k=6, g=3: jupyter file,
pdf file
- Case N=8, k=3, g=3: jupyter file,
pdf file
- Case N=9, k=2, g=3: jupyter file,
pdf file
- Case N=10, k=3, g=4: jupyter file,
pdf file
- Case N=11, k=6, g=7: jupyter file,
pdf file
- Case N=16, k=3, g=7: jupyter file,
pdf file
- Zapponi-orientable dessins d'enfants (with Gabino
González-Diez, Rubén Hidalgo y Gareth Jones). Rev. Mat. Iberoam.
36 (2020), no. 2, 549–570.
- Extremal disc packings in compact hyperbolic surfaces.
Rev. Mat. Complut. 31 (2018), no. 2, 467–478.
- Fields of definition of uniform dessins on quasiplatonic
surfaces (with David Torres-Téigell and Jürgen Wolfart).
Riemann and Klein surfaces, automorphisms, symmetries and moduli
spaces, 155–170, Contemp. Math., 629, Amer. Math. Soc.,
Providence, RI, 2014.
- Shimura curves with many uniform dessins (with David
Torres-Téigell and Jürgen Wolfart). Math. Z. 271 (2012),
no. 3-4, 757–779.
- Introduction to compact Riemann surfaces and dessins
d’enfants (with Gabino González-Diez). London
Mathematical Society Student Texts, 79. Cambridge University
Press, Cambridge, 2012.
- Genus 2 Belyi surfaces with a unicellular uniform dessin
(with David Torres). Geom. Dedicata 155 (2011), 81–103.
- On complex curves and complex surfaces defined over number
fields (with Gabino González Diez). Teichmüller theory
and moduli problem, 247–280, Ramanujan Math. Soc. Lect. Notes
Ser., 10, Ramanujan Math. Soc., Mysore, 2010.
- Right triangles with algebraic sides and elliptic curves
over number fields (with Gabino González-Diez, Enrique
González-Jimenez, Rasa Steuding and Jörn Steuding). Math.
Slovaca 59 (2009), no. 3, 299–306.
- Compact non-orientable hyperbolic surfaces with an
extremal metric disc (with Gou Nakamura). Conformal
Geometry and Dynamics 11 (2007), 29-43.
- A note on the action of the absolute Galois group on
dessins (with Gabino González-Diez). Bull. London Math.
Soc. 39 (2007), 721-723.
- On the structure of Whittaker sublocus of moduli space of
algebraic curves (with Gabino González-Diez). Proc. Roy.
Soc. Edinburgh Sect. A 136 (2006), no. 2, 337-346.
- Conjugators of Fuchsian groups and Quasiplatonic surfaces,
(with Jürgen Wolfart). Q. J. Math. 56 (2005),
no. 4, 525-540.
- Page containing
many figures related to this article (always under
construction).
- Effective Estimates for the Distribution of Values of
Euler Products, (with Jörn Steuding). Monatsh. Math. 145
(2005), no. 2, 97-106.
- On a conjecture of Whittaker concerning uniformization of
hyperelliptic curves (with Gabino González-Diez). Trans.
Amer. Mat. Soc. 356, Number 2 (2004), 691-702.
- Multiply Quasiplatonic Riemann Surfaces. Experimental
Mathematics 12:4 (2003), 463-475.
- Page containing the
programs (for GAP) and results of the computations concerning
this article.
- Genus 2 extremal surfaces: extremal discs, isometries and
Weierstrass points (with Gabino González-Diez). Israel J.
Math. 132 (2002), 221-238.
- On extremal Riemann surfaces and their uniformizing
Fuchsian groups (with Gabino González-Diez). Glasgow Math.
J. 44 (2002), 149-157.
- On extremal discs inside compact hyperbolic surfaces
(with Gabino González-Diez). C.R. Acad. Sci. Paris t. 329 Ser.
I, (1999), 57-60.