Yairon Cid-Ruiz

I am a postdoc at Ghent University in the Algebra Research Group.

Previously, I was a postdoc at the Max Planck Institute for Mathematics in the Sciences in the group led by Bernd Sturmfels.

Before that, I was a PhD student in the Universitat de Barcelona under the supervision of Carlos D'Andrea.

Here is my Curriculum Vitae.

Here is a copy of my PhD thesis.

Contact

Address: Department of Mathematics: Algebra and Geometry, Ghent University, Krijgslaan 281 – S25, 9000 Gent, Belgium.
Email: Yairon.CidRuiz at UGent dot be.


Research

My main research interest is commutative algebra and its interactions with algebraic geometry and combinatorics. I like topics related to blow-up algebras, local cohomology, multiplicities, symbolic powers, syzygies, regularity and edge ideals. I am particularly interested in the relations between blow-up algebras and certain criteria for the birationality of rational maps. Recently, I got interested on D-modules and its computational aspects.


Education


Publications & Preprints

  1. Bounding the degrees of a minimal μ-basis for a rational surface parametrization, Journal of Symbolic Computation 95 (2019), 134–150, journal version, arXiv:1611.07506.
  2. A D-module approach on the equations of the Rees algebra, to appear in Journal of Commutative Algebra, journal version, arXiv:1706.06215.
  3. Regularity and Gröbner bases of the Rees algebra of edge ideals of bipartite graphs, Le Matematiche Vol 73 No 2 (2018), pp. 279–296, journal version, arXiv:1801.06731.
  4. (with Sepehr Jafari, Beatrice Picone and Navid Nemati), Regularity of bicyclic graphs and their powers, Journal of Algebra and Its Applications 19 (2020), no. 3, 2050057, 38 pp., journal version, arXiv:1802.07202.
  5. (with Laurent Busé and Carlos D'Andrea), Degree and birationality of multi-graded rational maps, Proceedings of the London Mathematical Society (3) 121 (2020) 743–787, journal version, arXiv:1805.05180.
  6. Multiplicity of the saturated special fiber ring of height two perfect ideals, Proceedings of the American Mathematical Society 148 (2020), no. 1, 59–70, journal version, arXiv:1807.03189.
  7. (with Aron Simis), Degree of rational maps and specialization, International Mathematics Research Notices, rnaa183, 2020, journal version, arXiv:1901.06599.
  8. Noetherian operators, primary submodules and symbolic powers, Collectanea Mathematica 2020, journal version, arXiv:1909.07253.
  9. (with Vivek Mukundan), Multiplicity of the saturated special fiber ring of height three Gorenstein ideals, to appear in Acta Mathematica Vietnamica, journal version, arXiv:1909.13633.
  10. Mixed multiplicities and projective degrees of rational maps, to appear in Journal of Algebra, journal version, arXiv:2001.00547.
  11. (with Roser Homs and Bernd Sturmfels), Primary ideals and their differential equations, to appear in Foundations of Computational Mathematics, journal version, arXiv:2001.04700.
  12. (with Marc Chardin and Aron Simis), Generic freeness of local cohomology and graded specialization, to appear in Transactions of the American Mathematical Society, arXiv:2002.12053.
  13. (with Federico Castillo, Binglin Li, Jonathan Montaño and Naizhen Zhang), When are multidegrees positive?, Advances in Mathematics 374, 2020, journal version, arXiv:2005.07808.
  14. (with Jonathan Montaño), Convex bodies and graded families of monomial ideals, arXiv:2010.07918.
  15. (with Jonathan Montaño), Mixed mulitplicities of graded families of ideals, arXiv:2010.11862.
  16. Equations and multidegrees for inverse symmetric matrix pairs, arXiv:2011.04616.
  17. (with Justin Chen, Marc Härkönen, Robert Krone and Anton Leykin), Noetherian Operators in Macaulay2, arXiv:2101.01002.
  18. (with Bernd Sturmfels), Primary decomposition with differential operators, arXiv:2101.03643.

M2 codes


Research visits


Writings