Born in 1970 in Ezpeleta (Argentina), Martín Sombra studied Mathematics at the University of La Plata and obtained his PhD from the University of Buenos Aires with a thesis in Computer Algebra. He did postdoctoral stays at the MSRI in Berkeley, the IAS in Princeton, and the IMJ in Paris. He became Maître de Conférences at the University of Lyon 1, then spent four years as a "Ramón y Cajal" Researcher at the University of Barcelona (UB) and became afterwards Full Professor at the University of Bordeaux 1. He finally moved back to Barcelona in 2009, joining ICREA as a Research Professor and UB as a Profesor Asociado. He has also held visiting positions at the IPAM in Los Angeles, the MSRI in Berkeley, and the University of Buenos Aires. He is currently a member of the Board of Directors of the FoCM Society, and of the Advisory Board of the MEGA conferences.
Polynomials appear in a wide variety of contexts in Mathematics, Engineering and Computer Science. Polynomials in those situations are not random but come up with a certain structure which is important to exploit. I am interested in systems of structured polynomial equations and particularly in questions like: how many solutions does a given system have? How complicated those solutions can be? Can we predict where they will accumulate? Can we efficiently solve systems of polynomial equations? These problems have conduced me to study combinatorial objects like polytopes and fans, geometrical objects like curves and surfaces, and arithmetic objects like height of points and Diophantine equations. This gives a rich interplay between Complexity Theory, Combinatorics, Algebraic Geometry and Number Theory, leading to interesting results and stimulating research directions.
- Botero AM, Burgos Gil JI & Sombra M 2022, 'Convex analysis on polyhedral spaces', Mathematische Zeitschrift, 301, 1631-1674.
- Bilu Y, Burgos Gil JI & Sombra M 2022, 'La casa de los números pequeños', Gaceta de la Real Sociedad Matemática Española, vol. 25, pp. 577-575.
Selected research activities
- Talk at the Algebraic geometry seminar at Barcelona, 1 April
- Talk at the conference La grandezza dei punti piccoli at Pisa, Italy, 23-25 May
– Member of the board of directors of the FoCM Society
– Member of the advisory board of the series of conferences MEGA
– Member of the IMUB steering committee
– Coorganizer of the conference Intercity seminar on Arakelov Geometry at Madrid, 12-16 September
– Juan Brieva, undergraduate student at UPC participating at the summer program "Introduction to mathematical research"