Xavier Xarles

Associate professor at UAB
Research area: Number Theory

PhD in Mathematics obtained at UAB (1993)


I obtained my PhD in the UAB in 1993. As a postdoc I was in the University of Southern California and at the institute Henri Poincaré in Paris. I am Associate Professor at UAB since 1997.

Research lines

  • I work on arithmetic geometry, concretely on arithmetic of curves and abelian varieties
  • At present I am also interested in Nonarchimedean Analytic Geometries and Tropical Geometry

Selected publications

  • González Jiménez and X. Xarles On a conjecture of Rudin on squares in arithmetic progressions. LMS J. Comput. Math. 17 (2014), no. 1, 58-76.
  • X. Xarles,Trivial points on towers of curves. Journal de Théorie des Nombres de Bordeaux 25 (2013) 477-498.
  • E. González Jiménez and X. Xarles, Five squares in arithmetic progression over quadratic fields. Revista Matemática Iberoamericana 29, no. 4, 1211-1238 (2013).
  • X. Xarles, Squares in arithmetic progression over number fields. J. Number Theory 132 (2012), no. 3, 379-389.
  • O. Demchenko, A. Gurevich and X. Xarles, Formal completions of Néron models for algebraic tori. Proc. Lond. Math. Soc. (3) 100 (2010), no. 3, 607-638.