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ISEG  >  Matemática  >  ALBERTO LÓPEZ


    Research area

    My area of research in mathematics is algebraic geometry. Algebraic geometers study zero loci of systems of polynomials by looking at the interplay between the algebraic properties of the systems and the geometry of their solution set. These loci are called algebraic varieties. My focus is in the case when these varieties — and more general constructions called schemes — fall naturally into families that are themselves parametrized by other schemes — or stacks — called moduli or parameter spaces.


    Tropical geometry is at the interface between algebraic geometry, combinatorial optimization, and matroid theory. It has become a field of its own, and it is remarkable the broad number of its connections with other areas, such as computational biology or statistics. It has become a powerful tool as well within mathematics, especially in enumerative geometry, providing a bridge between symplectic geometry (which is the natural category in which to discuss Gromov-Witten invariants) and complex geometry. More recently, I have started to study its connections with problems in economics.


    Below is a list of my preprints and published papers. If you are interested in any of them and are not able to find it, just drop me an email!


    Coding theory

    > (with S. Cardell and J. J. Climent) SPC product codes, graphs with cycles and Kostka numbers, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113 (2019).

    Algebraic geometry

    > (with M. Chan, N. Pflueger, and M. Teixidor) Genera of Brill-Noether curves and staircase paths on Young tableaux, Trans. Amer. Math. Soc. 370 (2018).

    > (with A. Castorena and M. Teixidor) Petri map for vector bundles near good bundles, J. Pure Appl. Algebra 222 (2017).

    > (with M. Teixidor) Limit linear series on chains of elliptic curves and tropical divisors on chains of loops, Doc. Math. 22 (2017).

    > (with A. Castorena and M. Teixidor) Invariants of the Brill-Noether curve, Adv. Geom. 17 (2017).

    > Poincaré polynomials of stable map spaces to Grassmannians, Rend. Semin. Mat. Univ. Padova 131 (2014). 

    > Virtual normalization and virtual fundamental classes, Proc. Amer. Math. Soc. 140 (2012). 

    > Gromov-Witten invariants and rational curves on Grassmannians, Journal of Geometry and Physics 61 (2011).