Francesc Xavier Xarles Ribas

Francesc Xavier Xarles Ribas is a mathematician affiliated with the Department of Mathematics at Universitat Autònoma de Barcelona (UAB). He holds a Ph.D. in Mathematics from UAB (1993) and has held various academic positions including postdoctoral researcher at the University of Southern California and assistant roles at UAB since 1991. His research focuses on number theory, algebraic geometry, and arithmetic geometry, with contributions to topics like arithmetic progressions, p-adic groups, and number fields. He has been involved in multiple research projects funded by Spanish ministries, focusing on non-Archimedean valuations, effective methods in arithmetic geometry, and combinatorial approaches in algebraic geometry. Xarles has published extensively in peer-reviewed journals and contributed to collaborative projects across international institutions.

Education:

• Ph.D. in Mathematics, Universitat Autònoma de Barcelona, 1993
• Master’s in Mathematics, Universitat Autònoma de Barcelona, 1988

Research Interests: Number Theory, Algebraic Geometry, Arithmetic Geometry, p-adic Groups, Modular Curves, and Effective Methods in Arithmetic Geometry. His work bridges theoretical mathematics with computational approaches, emphasizing explicit valuations and geometric structures.

Recent Projects:

• VALORACIONES NO ARQUIMEDIANAS EN GEOMETRIA Y TEORIA DE NUMEROS EXPLICITAS (2021-2025)
• Métodos efectivos en Geometría Aritmética 2 (2016-2021)

Collaborations: Works with international researchers on modular curves, Iwasawa theory, and algebraic structures.