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

– D’Andrea C, Jeronimo G & Sombra M 2023 ‘The Canny-Emiris conjecture for the sparse resultant’, Foundations of Computational Mathematics, vol. 23, pp. 741-801.

Selected research activities

Invited talks
– Talk at the Arithmetic geometry seminar at Humboldt University Berlin, Germany,
31 January
– Talk at the Number theory seminar at Université de Caen, France, 24 March
– Talk at the conference XXXIèmes rencontres arithmétiques de Caen at Île de Tatihou, France, 26 June – 1 July
– Talk at the Number theory seminar at Universität Basel, Switzerland, 19 October
– Member of the board of directors of the FoCM Society
– Member of the advisory board of the series of conferences MEGA
– Coorganizer of the workshop Computational Algebraic Geometry at the conference FoCM 2023 at Paris, France, 12 – 21 June
– Member of the workshops and of the Stephen Smale committees of the
conference FoCM 2023 at Paris, France, 12 – 21 June
– Coorganizer (chair) of the conference
Global invariants of arithmetic varieties at CIRM, Marseille, France, 9 – 13 October
PhD and Master theses, and TFG’s
– Jury of the PhD thesis of Marcos Morales at Universidad Católica de Chile, Santiago, Chile, 27 March
– Jury of the PhD thesis of Njaka Andriamandratomanana at Université de Caen, France, 25 June
– Reviewer and jury of the PhD of Gerold Schefer at Universität Basel, Switzerland, 20 October