Research preprints and publications:
Abelian threefolds with imaginary multiplication (with P. Goodman), submitted.
Geometrically simple counterexamples to a local-global principle for quadratic twists (with E. Ambrosi, N. Coppola), submitted.
Abelian varieties genuinely of GLn-type (with E. Florit, X. Guitart), submitted.
Frobenius sign separation for abelian varieties (with A. Bucur, K.S. Kedlaya), to appear in Proc. Amer. Math. Soc.
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), Indiana Univ. Math. J. 73 (2024), no. 6, 2135--2154.
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 Mem. Amer. Math. Soc.
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), J. Eur.
Math. Soc. 26 (2024), 1713--1746.
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 (with X. Guitart) to Fabien Narbonne's article: Polarized products of elliptic curves with complex multiplication and field of moduli Q, Polynesian Journal of Mathematics, Volume 1 Issue 5 (2024), 1--33.
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:
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.
UNSW Number Theory Days, University of New South Wales, Sydney, August 13--14, 2025.
René 25, University of the French Polynesia, Tahiti, August 18--22, 2025.
Curves, Abelian VArieties, and RElated Topics, Universitat de Barcelona, Barcelona, July 13--17, 2026.
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 April 16, 2025
|
