Research

Papers:

• Bianchi and Hilbert-Blumenthal quaternionic orbifolds (joint with A. Verjovsky). Geom. Dedicata 217, Article number:108 (2023) (arXiv, Journal).

• Automorphic Galois representations and the inverse Galois problem for certain groups of type D_m. Proc. Amer. Math. Soc. 149 (2021), 89-95 (arXiv, Journal). 

• Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups. J. Number Theory 206 (2020), 182-193 (arXiv, Journal).  

• On the images of the Galois representations attached to generic automorphic representations of GSp(4) (joint with L. Dieulefait). Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 20 (2020), no. 2, 635-655 (arXiv, Journal).  

• On the images of the Galois representations attached to some RAESDC automorphic representations of GLn(AQ), Math. Res. Lett.  26 (2019), no. 3, 921-947. (arXiv, Journal).

• Constructing Hilbert modular forms without exceptional primes (joint with L. Dieulefait). Math. Z. 288 (2018), 199-215. (arXiv, Journal). 

Preprints or submitted papers:

• Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$ (joint with L. Gutiérrez-Frez). Submitted (arXiv).

• Galois representations with large image in Langlands correspondence. Submitted (arXiv).  

• On the images of G_2-valued automorphic Galois representations. Preprint (arXiv).

In progress (preprints available upon request):

• with V. C. Garcia, On arithmetic properties of coefficients of Hilbert modular forms on finite fields.

• with T. M. Gendron, 𝛉-adic arithmetic and quasicrystalline schemes. 

Thesis:

• On the images of the Galois representations associated to certain automorphic forms. (.pdf) Ph.D. thesis, UNAM (2017). 

• Sur l'image des représentations galoisiennes attachées aux formes modulaires de Siegel de genre 2. (.pdf on demand) Mémoire M2, École Polytechnique (2012).

• Una descripción de las extensiones abelianas de un campo cuadrático imaginario. (.pdf) Master thesis, UNAM (2011).

• Campos de números no lineales. (.pdf) Bachelor thesis, UNAM (2009). Honourable mention (Sotero Prieto 2010) by the SMM.

Scientific outreach in Spanish:

• Perfectoides: la revolucionaria idea de Peter Scholze. Motivos matemáticos 1 (2018) no. 3. (Journal). 

• El programa de Langlands y su aplicación al problema inverso de la teoria de Galois. Accepted in Revista Mixba'al.

ORCID-ID: https://orcid.org/0000-0002-6379-7294