I did my PhD at the UPC under the direction of Jordi Quer. I did postdocs at the Max Planck Institute for Mathematics at Bonn, the University of Duisburg-Essen, and the UB.

Personal webpage: http://www.maia.ub.es/~guitart/

• Rational points on elliptic curves, Heegner points, Stark-Heegner points (with emphasis on their effective computation).
• Modular abelian varieties, abelian varieties of GL2 -type, Q-curves.
  
  

Endomorphism algebras of geometrically split abelian surfaces over Q.
F. Fité, X. Guitart. Algebra and Number Theory Vol. 14 (2020), No. 6, 1399-1421

Fields of definition of elliptic k-curves and the realizability of all genus 2 Sato-Tate groups over a number field.
F. Fité, X. Guitart. Trans. Amer. Math. Soc. Vol. 370, N. 7 (2018), 4623-4659

Darmon points on elliptic curves over number fields of arbitrary signature.
X. Guitart, M. Masdeu, and H. Sengun. P. Lond. Math. Soc. (3) 111 (2015), no. 2, 484-518.

Overconvergent cohomology and quaternionic Darmon points.
X. Guitart, M. Masdeu. J. Lond. Math. Soc. (2) 90 (2014), no. 2, 495--524.

Almost totally complex points on elliptic curves.
X. Guitart, V. Rotger, and Y. Zhao. Trans. Amer. Math. Soc. 336 (2014), 2773-2802