Publications

Published or accepted papers:

  • with Eran Assaf and Elisa Lorenzo García, On smooth plane models for modular curves of Shimura type, ANTS-XV proceedings, Research in Number Theory, to appear, 2022 (arxiv link)

  • with Vladimir Dokchitser, Constructing hyperelliptic curves with surjective Galois representations, Transactions of the American Mathematical Society, 2020, 373 (2), pp. 1477-1500, American Mathematical Society, doi:10.1090/tran/7995 (arxiv link)

  • with Gebhard Boeckle, Peter Mathias Graef and Alvaro Troya, Computing $\mathcal{L}$-invariants via the Greenberg-Stevens formula, Journal de Théorie des Nombres de Bordeaux, 2019, 31 (3), pp. 727-746, doi:10.5802/jtnb.1106 (arxiv link)

  • A note on the minimal level of realization for a mod $\ell$ eigenvalue system, Automorphic forms and related topics, Contemporary Mathematics, 2019, 732, pp. 1–13, American Mathematical Society, (arXiv link)

  • with Pedro Lemos and Samir Siksek, Residual Representations of Semistable Principally Polarized Abelian Varieties, Research in Number Theory 2016, doi:10.1007/s40993-015-0032-4 (arXiv link)

  • with Samir Siksek, Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2ℓ}+y^{2m}=z^p$, Algebra & Number Theory, 2016, 10 (6), pp. 1147-1172; doi: 10.2140/ant.2016.10.1147 (arXiv link)

  • with Samir Siksek, On Serre's uniformity conjecture for semistable elliptic curves over totally real fields, Mathematische Zeitschrift 2015; doi:10.1007/s00209-015-1478-8 (arxiv link)

  • A local-global principle for isogenies of prime degree over number fields, Journal of the London Mathematical Society 2014; doi: 10.1112/jlms/jdu002 (arXiv link)


Book

  • with Valentijn Karemaker and Elisa Lorenzo García, Arithmetic, Geometry, Cryptography, and Coding Theory 2021, Contemporary Mathematics vol. 779, AMS, 2022, ISBNs: 978-1-4704-6794-4 (print); 978-1-4704-7089-0 (online) DOI: https://doi.org/10.1090/conm/779 (AMS website)

  • with J. Jorgenson, L. Smajlović, L. Walling, Automorphic Forms and Related Topics, Contemporary Mathematics, 2019; Volume 732, ISBNs: 978-1-4704-3525-7 (print); 978-1-4704-5317-6 (online), DOI: https://doi.org/10.1090/conm/732


Preprints or submitted papers:

  • with Alexandru Ghitza and Anna Medvedovsky, Deep congruences + the Brauer-Nesbitt theorem (arxiv link)

  • with Vladimir Dokchitser, $\ell$-Adic Representations and their Associated Invariants, lecture notes (arxiv link)


In progress (preprints available upon request):

  • with Peter Bruin, Checking isomorphisms of residual modular Galois representations

  • with Alexandru Ghitza and Anna Medvedovsky, Refined dimensions of Atkin–Lehner eigenspaces

  • with Luca Notarnicola, An arithmetic study of Edwards curves

  • with Eduardo Soto, A computational study of Hecke eigenvalue fields

  • with Paloma Bengoechea, Hecke eigenvalues of Hilbert modular forms and a generalization of Maeda's Conjecture

  • with Vandita Patel, Congruence graphs and Hecke algebras, see here

  • with Alyson Deines, Discriminant twins over totally real number fields

  • Twists and local data of residual modular Galois representations, see here


Ph.D. thesis:

  • Images of Galois representations, Ph.D. thesis, avaliable here.