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Martín Sombra

Martín Sombra

Universitat de Barcelona

Experimental Sciences & Mathematics

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.

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

Sombra M & Yger, A, ‘Bounds for multivariate residues and for the polynomials in the elimination theorem’, Moscow Mathematical Journal 21 (2021) 129-173.

Selected research activities

Invited talks

– Talk (online) at the Mathematical Congress of the Americas (MCA 2021) at Buenos Aires, 19-21 July

– Talk at the conference Arakelov Geometry at Regensburg, 6-10 September

– Talk (online) at the Number theory web seminar, 16 September

– Talk (online) at the Seminario del CMaLP at La Plata, 12 November

– Talk (online) at the conference Symbolic and numerical algorithms in algebraic geometry at Buenos Aires, 13-15 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

– Member of the review panel of a DFG Collaborative Research Center/Transregio, Germany

– Coorganizer of the conference Symbolic and numerical algorithms in algebraic geometry at Buenos Aires, 13-15 December

PhD and Master theses, and TFG’s

– Andriana Karuk, ‘Unlikely intersections in dynamics’ at UB, 4 February

– Marta Fernández, ‘ Aproximació als conjunts de Julia i de Mandelbrot’ at UB, 6 July

– Reviewer and member of the jury of the PhD thesis of Milan Perera at Université de Paris, 7 May

ICREA Memoir 2021