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 local-global principle for polyquadratic twists of abelian surfaces (with A. Perucca), to appear in the Indiana University Mathematics Journal.
On a local-global principle for quadratic twists of abelian varieties, Math. Ann. 388, pages 769--794, (2024).
Sato-Tate groups of abelian threefolds (with K.S. Kedlaya and A.V. Sutherland), to appear in Memoirs of the American Mathematical Society.
Computing L-Polynomials of Picard curves from Cartier-Manin matrices. With an appendix by A.V. Sutherland (with S. Asif, D. Pentland), Math. Comp. 91 (2022), no. 334, 943--971.
Ordinary primes for some varieties with extra endomorphisms, Pub. Mat. 68 (2024), 27--40.
Effective Sato-Tate conjecture for abelian varieties and applications (with A. Bucur, K.S. Kedlaya), to appear in Journal of the European Mathematical Society.
Sato-Tate groups of abelian threefolds: a preview of the classification (with K. S. Kedlaya, A.V. Sutherland), Contemp. Math. 770 (2021), 103--129.
Arithmetic invariants from Sato-Tate moments (with E. Costa, A.V. Sutherland), C. R. Math. Acad. Sci. Paris 357 (2019), 823--826.
Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of GL2-type (with X. Guitart), Mathematische Zeitschrift 300 (2022), 2975--2995.
Endomorphism algebras of geometrically split abelian surfaces over Q (with X. Guitart), Algebra Number Theory 14 n. 6 (2020), 1399--1421.
On the Hilbert eigenvariety at exotic and CM classical weight 1 points (with A. Betina, S.V. Deo), Mathematische Zeitschrift 298 (3) (2021), 1077--1096.
Sato-Tate 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 Sato--Tate measure (with X. Guitart), Int. Math. Res. Not. IMRN, Volume 2019, Issue 13, July 2019, Pages 4081--4118.
Del Pezzo surfaces over finite fields and their Frobenius traces (with B. Banwait, D. Loughran), Math. Proc. Cambridge Philos. Soc. 167 (2019), 35-60. Code.
Fields of definition of elliptic k-curves and the realizability of all genus 2 Sato-Tate groups over a number field (with X. Guitart), Trans. Amer. Math. Soc. 370, n. 7 (2018), 4623--4659. Erratum.
Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx (with A.V. Sutherland), Contemp. Math. 663 (2016), 103--126.
On the singularity of the Demjanenko matrix of quotients of Fermat curves (with I.E. Shparlinski), Proc. Amer. Math. Soc. 144 (2016), no. 1, 55--63.
Equidistribution, L-functions, and Sato-Tate groups, Contemp. Math. 649 (2015), 63--88.
Frobenius distribution for quotients of Fermat curves of prime exponent (with J. González, J.-C. Lario), Canad. J. Math. 68 n. 2 (2016), 361--394.
Sato-Tate groups of some weight 3 motives (with K.S. Kedlaya and A.V. Sutherland), Contemp. Math. 663 (2016), 57--101.
Sato-Tate distributions of twists of y^2=x^5-x and y^2=x^6+1 (with A.V. Sutherland), Algebra Number Theory 8 n. 3 (2014), 543--585.
Sato-Tate distributions and Galois endomorphism modules in genus 2 (with K.S. Kedlaya, A.V. Sutherland, V. Rotger), Compos. Math. 148 n. 5 (2012), 1390--1442.
The twisting representation of the L-function of a curve (with J-C. Lario), Rev. Mat. Iberoam., 29 n. 3 (2013), 749--764.
Artin representations attached to pairs of isogenous abelian varieties, J. Number Theory 133 n. 4 (2013), 1331--1345.
Other contributions:
Appendix to Christian Johansson's article: On the Sato-Tate conjecture for non-generic abelian surfaces, Trans. Amer. Math. Soc. 369 (2017), 6303--6325.
Appendix to Joan-Carles Lario and Anna Somoza's article: The Sato-Tate conjecture for a Picard curve with complex multiplication, Contemp. Math. 701 (2018), 151--165.
Expository note: Sèries de Dirichlet associades a formes modulars de Siegel, Notes del Seminari de Teoria de Nombres UB-UAB-UPC, Bayer-Nart-Quer, ISBN: 978-84-934244-7-3, Barcelona, 2009.
Talks in conferences or seminars
Some past conferences attended
Teaching
Research and learning seminars
Coming events:
Birational geometry: from moduli to geography, Universitat de Barcelona, February 5--7, 2025.
Arithmetic, Geometry, Cryptography and Coding Theory (AGCT), CIRM, Luminy, June 9--13, 2025.
33èmes Journées arithmétiques 2025, University of Luxembourg, Esch-sur-Alzette, June 30--July 4, 2025.
CV
I did my thesis within the Number Theory Research Group of Universitat Politècnica de Catalunya (UPC), under the supervision of Joan-C. 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 Duisburg-Essen, and UPC/BGSmath. I was a member at the Institute for Advanced Study for the academic year 2018-19 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 October 17, 2024
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