Research preprints and publications:
Sato-Tate distributions of twists of the Fermat and the Klein quartics (with E. Lorenzo, A.V. Sutherland), submitted.
On the rank and the convergence rate towards the Sato--Tate measure (with X. Guitart), to appear in I.M.R.N.
Del Pezzo surfaces over finite fields and their Frobenius traces (with B. Banwait, D. Loughran), to appear in Mathematical Proceedings of the Cambridge Philosofical Society. 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), Transactions of the American Mathematical Society 370, n. 7 (2018), 4623--4659.
Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx (with A.V. Sutherland), Contemporary Mathematics 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.
Some instances of the effective Sato-Tate conjecture (with A. Bucur, K.S. Kedlaya), preprint.
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), Contemporary Mathematics 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), Compositio Mathematica 148 n. 5 (2012), 1390--1442.
The twisting representation of the L-function of a curve (with J-C. Lario), Revista Matemática Iberoamericana, 29 n. 3 (2013), 749--764.
Artin representations attached to pairs of isogenous abelian varieties, Journal of Number Theory 133 n. 4 (2013), 1331--1345.
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, Contemporary Mathematics 701 (2018), 151--165.
Expository note: Galois representations associated to ordinary Hibert modular forms: Wiles' theorem, to appear in Notes del Seminari de Teoria de Nombres UB-UAB-UPC.
Expository note: Equidistribution, L-functions, and Sato-Tate groups, Contemporary Mathematics 649 (2015), 63--88.
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.
New pictures of old paintings
Talks in conferences or seminars
Some past conferences attended
Arithmetic of curves, Baskerville Hall, Hay-on-Wye, 13--17 August, 2018.
Arithmetic Geometry, Number Theory, and Computation, MIT, Cambridge (Massachussets), 20--24 August, 2018.
I did my thesis within the Number Theory Research Group of Universitat Politècnica de Catalunya, 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 for 2,5 years. After this, I was a postdoc at the University of Duisburg-Essen for 2 years. I am heartfully thankful to the institutions and individuals that have welcomed me during all these years.
Last modified on 17th April 2018