Research preprints and publications:
Frobenius sign separation for abelian varieties (with A. Bucur, K.S. Kedlaya), submitted.
Endomorphism algebras of geometrically split genus 2 Jacobians over Q (with E. Florit, X. Guitart), submitted.
A localglobal principle for polyquadratic twists of abelian surfaces (with A. Perucca), to appear in the Indiana University Mathematics Journal.
On a localglobal principle for quadratic twists of abelian varieties, Math. Ann. 388, pages 769794, (2024).
SatoTate groups of abelian threefolds (with K.S. Kedlaya and A.V. Sutherland), to appear in Memoirs of the American Mathematical Society.
Computing LPolynomials of Picard curves from CartierManin matrices. With an appendix by A.V. Sutherland (with S. Asif, D. Pentland), Math. Comp. 91 (2022), no. 334, 943971.
Ordinary primes for some varieties with extra endomorphisms, Pub. Mat. 68 (2024), 2740.
Effective SatoTate conjecture for abelian varieties and applications (with A. Bucur, K.S. Kedlaya), to appear in Journal of the European Mathematical Society.
SatoTate groups of abelian threefolds: a preview of the classification (with K. S. Kedlaya, A.V. Sutherland), Contemp. Math. 770 (2021), 103129.
Arithmetic invariants from SatoTate moments (with E. Costa, A.V. Sutherland), C. R. Math. Acad. Sci. Paris 357 (2019), 823826.
Tate module tensor decompositions and the SatoTate conjecture for certain abelian varieties potentially of GL_{2}type (with X. Guitart), Mathematische Zeitschrift 300 (2022), 29752995.
Endomorphism algebras of geometrically split abelian surfaces over Q (with X. Guitart), Algebra Number Theory 14 n. 6 (2020), 13991421.
On the Hilbert eigenvariety at exotic and CM classical weight 1 points (with A. Betina, S.V. Deo), Mathematische Zeitschrift 298 (3) (2021), 10771096.
SatoTate distributions of twists of the Fermat and the Klein quartics (with E. Lorenzo, A.V. Sutherland), Res. Math. Sci. 5 (2018), 41 pages.
On the rank and the convergence rate towards the SatoTate measure (with X. Guitart), Int. Math. Res. Not. IMRN, Volume 2019, Issue 13, July 2019, Pages 40814118.
Del Pezzo surfaces over finite fields and their Frobenius traces (with B. Banwait, D. Loughran), Math. Proc. Cambridge Philos. Soc. 167 (2019), 3560. Code.
Fields of definition of elliptic kcurves and the realizability of all genus 2 SatoTate groups over a number field (with X. Guitart), Trans. Amer. Math. Soc. 370, n. 7 (2018), 46234659. Erratum.
SatoTate groups of y^2=x^8+c and y^2=x^7cx (with A.V. Sutherland), Contemp. Math. 663 (2016), 103126.
On the singularity of the Demjanenko matrix of quotients of Fermat curves (with I.E. Shparlinski), Proc. Amer. Math. Soc. 144 (2016), no. 1, 5563.
Equidistribution, Lfunctions, and SatoTate groups, Contemp. Math. 649 (2015), 6388.
Frobenius distribution for quotients of Fermat curves of prime exponent (with J. González, J.C. Lario), Canad. J. Math. 68 n. 2 (2016), 361394.
SatoTate groups of some weight 3 motives (with K.S. Kedlaya and A.V. Sutherland), Contemp. Math. 663 (2016), 57101.
SatoTate distributions of twists of y^2=x^5x and y^2=x^6+1 (with A.V. Sutherland), Algebra Number Theory 8 n. 3 (2014), 543585.
SatoTate distributions and Galois endomorphism modules in genus 2 (with K.S. Kedlaya, A.V. Sutherland, V. Rotger), Compos. Math. 148 n. 5 (2012), 13901442.
The twisting representation of the Lfunction of a curve (with JC. Lario), Rev. Mat. Iberoam., 29 n. 3 (2013), 749764.
Artin representations attached to pairs of isogenous abelian varieties, J. Number Theory 133 n. 4 (2013), 13311345.
Other contributions:
Appendix to Christian Johansson's article: On the SatoTate conjecture for nongeneric abelian surfaces, Trans. Amer. Math. Soc. 369 (2017), 63036325.
Appendix to JoanCarles Lario and Anna Somoza's article: The SatoTate conjecture for a Picard curve with complex multiplication, Contemp. Math. 701 (2018), 151165.
Expository note: Sèries de Dirichlet associades a formes modulars de Siegel, Notes del Seminari de Teoria de Nombres UBUABUPC, BayerNartQuer, ISBN: 9788493424473, Barcelona, 2009.
Talks in conferences or seminars
Some past conferences attended
Teaching
Seminar talks in Barcelona
Coming events:
The Mordell conjecture 100 years later, Massachusetts Institute of Technology, Cambridge, July 812, 2024.
ANTS XVI, Massachusetts Institute of Technology, Cambridge, July 1519, 2024.
CV
I did my thesis within the Number Theory Research Group of Universitat Politècnica de Catalunya (UPC), under the supervision of JoanC. Lario. After short research stays at the University of Cambridge, MIT and UCSD, I was a postdoc at the University of Bielefeld, the University of DuisburgEssen, and UPC/BGSmath. I was a member at the Institute for Advanced Study for the academic year 201819 and then a research scientist at MIT from 2019 until 2021. I am heartfully thankful to the institutions and individuals that have welcomed me during all these years.
Last modified on June 26, 2024
