Martín Sombra

Universitat de Barcelona

Experimental Sciences & Mathematics

Born in 1970 in Ezpeleta (Argentina), Martín Sombra studied Mathematics as an undergraduate at the University of La Plata. He did his PhD thesis on Computer Algebra at the University of Buenos Aires. He then did postdoctoral stays at the MSRI at Berkeley, the IAS at Princeton, and the IMJ at 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, and became afterwards Full Professor at the University of Bordeaux 1. He finally moved back to Barcelona, joining ICREA in 2009. He works on problems at the interface of Algebraic Geometry, Number Theory and Complexity Theory. He currently collaborates with research groups in Barcelona, Paris, Caen, Bordeaux and Buenos Aires.

Research interests

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.

Selected publications

- D'Andrea C, Narváez-Clauss M & Sombra M 2017, 'Quantitative equidistribution of Galois orbits of small points in the N-dimensional torus', Algebra & Number Theory, vol. 11, pp 1627-1655.  

- Amoroso A, Sombra M & Zannier U 2017, 'Unlikely intersections and multiple roots of sparse polynomials', Mathematische Zeitschrift 287, 1065-1081.

Selected research activities

Invited talks (selected)

- Plenary talk at the conference "Effective methos in algebraic geometry" (MEGA 2017) at Nice, France, 12 - 16 June

- Mini-course at the CIMPA research school "Géométrie complexe et applications" at Ziguinchor, Senegal, 27 November - 1 December

- Plenary talk at the RSME-UMA joint meeting at Buenos Aires, Argentina, 11 - 15 December


- Conference "Foundations of computational mathematics" (FoCM 2017) at UB, 10 - 19 July (main organizer)

- IMUB colloquium

- CIMPA research school "Géométrie complexe et applications" at Ziguinchor, Senegal, 27 November - 1 December


- 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

Supervision of PhD thesis

- César Martínez, "Two problems in arithmetic geometry. Explicit Manin-Mumford, and arithmetic Bernštein-Kušnirenko", UB & Université de Caen, France, 29 September (joint with F. Amoroso)