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.
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.
– D’Andrea C, Ostafe A., Shparlinski IE & Sombra M 2019, ‘Reduction modulo primes of systems of polynomial equations and algebraic dynamical systems’, Transactions of the American Mathematical Society, vol. 371, pp. 1169-1198.
– Burgos Gil JI, Philippon P, Rivera-Letelier J & Sombra M 2019, ‘The distribution of Galois orbits of points of small height in toric varieties’, American Journal of Mathematics, vol. 141, pp. 309-381.
– Amoroso F & Sombra M 2019, ‘Factorization of bivariate sparse polynomials’, Acta Arithmetica, 191, 4, 361 – 381.
– Martinez C & Sombra M 2019, ‘An arithmetic Berntein-Kunirenko inequality’, Mathematische Zeitschrift, 291, 3-4, 1211 – 1244.
Selected research activities
Cohen A, Dahmen W, Munthe-Kaas H, Sombra M & Szanto A (editors), ‘Special issue on the occasion of the FoCM 2017 conference’, Foundations of Computational Mathematics 19 (2019) 963-1190.
– Talk at the ‘BGSMath María de Maeztu unit of excellence closing workshop’ at UB, 6 June
– Talk at the conference ‘Complexity of numerical computation’ at Berlin, 19 – 23 August
– Seminar talks at U. Regensburg (Germany), U. Rochester (USA) and ICMAT (Madrid)
– 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 Master thesis
– Sergi Rovira, ‘The polynomial method over varieties’, UB, 26 September
— Taller al ‘Dia internacional de la dona i la nena a la ciència 2018’, IEC, 14 February