Martín Sombra

Full professor at UB
Research area: Algebra / Geometry

PhD in Mathematics obtained at Universidad de Buenos Aires, Argentina (1998)


He studied Mathematics as an undergraduate at U. La Plata (1988-1992) and did a Ph.D thesis at U. Buenos Aires (1993-1998). He an ICREA Research Professor at Universitat de Barcelona since 2009.

His main scientific achievements are the development of the arithmetic geometry of toric varieties (jointly with J. I. Burgos and P. Philippon) and the effective versions of Hilbert’s Nullstellensatz (partly with C. D’Andrea and T. Krick).

In 2007, he received the “Journal of Complexity Best Paper Award”.

He is member of the Advisory Board of the series of international conferences “Effective Methods in Algebraic Geometry” (MEGA), and a member of the Steering Committee of the Institut de Matemàtiques de la UB (IMUB).

Research lines

  • Algebraic and Diophantine geometry
  • Arakelov geometry
  • Computer algebra
  • Discrete geometry

Selected publications

  • Arithmetic geometry of toric varieties. Metrics, measures and heights (with J. I. Burgos Gil and P. Philippon). Astérisque 360, Société Mathématique de France, 2014, vi + 222 pages
  • Quantitative equidistribution for the solutions of a system of sparse polynomial equations (with C. D’Andrea and A. Galligo). American Journal of Mathematics 136 (2014) 1543-1579
  • Height of varieties in multiprojective spaces and arithmetic Nullstellensätze (with C. D’Andrea and T. Krick). Annales Scientifiques de l’École Normale Supérieure 46 (2013) 549-627
  • Factoring bivariate sparse (lacunary) polynomials (with M. Avendaño and T. Krick). Journal of Complexity 23 (2007) 193-216
  • Sharp estimates for the arithmetic Nullstellensatz (with T. Krick and L. M. Pardo). Duke Mathematical Journal 109 (2001) 521-598