Martín Sombra is an ICREA Research Professor at UB. He did a PhD thesis at the University of Buenos Aires, and postdoctoral stays at the MSRI at Berkeley, the IAS at Princeton, and the IMJ at Paris. He was also a Maître de Conférences at the University of Lyon, and a Full Professor at the University of Bordeaux. He is a member of the Board of Directors of the FoCM Society, and of the Advisory Board of the MEGA conferences. He currently works on problems at the interface of Algebraic Geometry, Number Theory and Complexity Theory, and collaborates with research groups in Barcelona, Madrid, Paris, Caen, Bordeaux, Santiago de Chile and Rochester.
Personal webpage: http://www.maia.ub.es/~sombra/
- Diophantine geometry
- Arakelov geometry
- Computer algebra
- Discrete geometry
- 2020-2023 National Program of Research of the Spanish Ministery of Science and Innovation PID2019-104047GB-I00 Algebraic, Linear and Differential Geometry. Theory and Applications.
10 most important publications in the last 10 years. Complete list in http://www.maia.ub.es/~sombra/publications.html
C. D'Andrea, G. Jeronimo, and M. Sombra, The Canny-Emiris conjecture for the sparse resultant, to appear in Foundations of Computational Mathematics, 52 pages.
M. Sombra and A. Yger, Bounds for multivariate residues and for the polynomials in the elimination theorem, Moscow Mathematical Journal 21 (2021) 129-173.
J. I. Burgos Gil, P. Philippon, J. Rivera-Letelier, and M. Sombra, The distribution of Galois orbits of points of small height in toric varieties, American Journal of Mathematics 141 (2019) 309-381.
C. D'Andrea, A. Ostafe, I. E. Shparlinski, and M. Sombra, Reduction modulo primes of systems of polynomial equations and algebraic dynamical systems, Transactions of the American Mathematical Society 371 (2019) 1169-1198.
S. Basu and M. Sombra, Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions, Discrete & Computational Geometry 55 (2016) 158-184.
J. I. Burgos Gil, A. Moriwaki, P. Philippon, and M. Sombra, Arithmetic positivity on toric varieties, Journal of Algebraic Geometry 25 (2016) 201-272.
- C. D'Andrea and M. Sombra, A Poisson formula for the sparse resultant, Proceedings of the London Mathematical Society 11 (2015) 932-964.
F. Amoroso, L. Leroux, and M. Sombra, Overdetermined systems of sparse polynomial equations, Foundations of Computational Mathematics 15 (2015) 53-87.
J. I. Burgos Gil, P. Philippon, and M. Sombra, Arithmetic geometry of toric varieties. Metrics, measures and heights, Astérisque 360, Société Mathématique de France, 2014, vi + 222 pages, ISBN 978-2-85629-783-4.
C. D'Andrea, T. Krick, and M. Sombra, Height of varieties in multiprojective spaces and arithmetic Nullstellensätze, Annales Scientifiques de l'École Normale Supérieure 46 (2013) 549-627.