Yairon Cid-Ruiz

I am an Assistant Professor in the Department of Mathematics at North Carolina State University.

I was an FWO postdoctoral fellow at KU Leuven. Previously, I was a postdoc at Ghent University and the Max Planck Institute for Mathematics in the Sciences in the group led by Bernd Sturmfels. Before that, I was a PhD student at the Universitat de Barcelona under the supervision of Carlos D'Andrea.

Here is my Curriculum Vitae.

Contact

Address: Department of Mathematics, SAS Hall 4214, North Carolina State University, Box 8205 Raleigh, NC 27695 USA.
Email: ycidrui at ncsu dot edu.

Research

My main research interests lie in commutative algebra and algebraic geometry. I like topics related to blow-up algebras, local cohomology, multiplicities, differential operators, Hilbert schemes, symbolic powers, syzygies, regularity and edge ideals.

Publications & Preprints

0. Blow-up algebras in Algebra, Geometry and Combinatorics, PhD thesis, Univesitat de Barcelona (2019).
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,
   Journal of Commutative Algebra Vol 14 (2022), No. 2, 155-176, 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 72, pp. 175–202 (2021), journal version, arXiv:1909.07253.
9. (with Vivek Mukundan), Multiplicity of the saturated special fiber ring of height three Gorenstein ideals,
   Acta Mathematica Vietnamica 46, pp. 663–674 (2021), journal version, arXiv:1909.13633.
10. Mixed multiplicities and projective degrees of rational maps,
    Journal of Algebra 566 (2021) pp. 136–162, journal version, arXiv:2001.00547.
11. (with Roser Homs and Bernd Sturmfels), Primary ideals and their differential equations,
    Foundations of Computational Mathematics 21, pp. 1363–1399 (2021), journal version, arXiv:2001.04700.
12. (with Marc Chardin and Aron Simis), Generic freeness of local cohomology and graded specialization,
    Transactions of the American Mathematical Society 375 (2022), no. 1, 87–109, journal version, 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,
    Revista Matemática Iberoamericana 38 (2022), no. 6, 2033–2056, journal version, arXiv:2010.07918.
15. (with Jonathan Montaño), Mixed mulitplicities of graded families of ideals,
    Journal of Algebra 590 (2022) 394–412, journal version, arXiv:2010.11862.
16. Equations and multidegrees for inverse symmetric matrix pairs,
    Le Matematiche Vol. LXXVI (2021) - Issue II, pp. 369–381, journal version, arXiv:2011.04616.
17. (with Justin Chen, Marc Härkönen, Robert Krone and Anton Leykin), Noetherian Operators in Macaulay2,
    Journal of Software for Algebra and Geometry Vol. 12 (2022), 33–41, journal version, arXiv:2101.01002.
18. (with Bernd Sturmfels), Primary decomposition with differential operators,
    International Mathematics Research Notices, rnac178, 2022, journal version, arXiv:2101.03643.
19. (with Justin Chen), Primary decomposition of modules: a computational differential approach,
    Journal of Pure and Applied Algebra 226, 2022, journal version, arXiv:2104.03385.
20. (with Fatemeh Mohammadi and Leonid Monin), Multigraded algebras and multigraded linear series,
    Journal of the London Mathematical Society, Volume 109, Issue 3 (2024), journal version, arXiv:2104.05397.
21. Fiber-full modules and a local freeness criterion for local cohomology modules,
    Mathematische Zeitschrift 303, 30 (2023), journal version, arXiv:2106.07777.
22. (with Ritvik Ramkumar), The fiber-full scheme, arXiv:2108.13986.
23. (with Federico Castillo, Fatemeh Mohammadi and Jonathan Montaño), Double Schubert polynomials do have saturated Newton polytopes,
    Forum of Mathematics, Sigma (2023), Vol. 11:e100 1–9, journal version, arXiv:2109.10299.
24. (with Oliver Clarke and Fatemeh Mohammadi), A study of nonlinear multiview varieties,
    Journal of Algebra 620 (2023) 363–391, journal version, arXiv:2112.06216.
25. (with Ritvik Ramkumar), A local study of the fiber-full scheme,
    Journal of Algebra 636 (2023) 248–278, journal version, arXiv:2202.06652.
26. (with Claudia Polini and Bernd Ulrich), Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras,
    Journal für die reine und angewandte Mathematik (Crelle's journal) (to appear), arXiv:2205.03837.
27. (with Alessio Caminata and Aldo Conca), Multidegrees, prime ideals, and non-standard gradings,
    Advances in Mathematics 435 (2023) 109361, journal version, arXiv:2208.07238.
28. (with Federico Castillo, Fatemeh Mohammadi and Jonathan Montaño), K-polynomials of multiplicity-free varieties, arXiv:2212.13091.
29. (with Ilya Smirnov), Effective generic freeness and applications to local cohomology,
    Journal of the London Mathematical Society, Volume 110, Issue 4 (2024), journal version, arXiv:2302.08196.
30. Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities, arXiv:2311.15105.
31. Polar multiplicities and integral dependence,
    International Mathematics Research Notices 2024, 00(0), 1–18, journal version, arXiv:2401.10198.
32. (with Jack Jeffries), Uniformity in nonreduced rings via Noetherian operators, arXiv:2404.02057.
33. (with Claudia Polini and Bernd Ulrich), Multidegrees, families, and integral dependence, arXiv:2405.07000.

M2 codes

• Related to “Degree and birationality of multi-graded rational maps”:
  • A package for computing the degree and checking the birationality of a multi-graded rational map: MultiGradedRationalMap.m2.
  • A list of examples using this package: degComputationExamples.m2.
• Related to “Primary ideals and their differential equations”: https://mathrepo.mis.mpg.de/PrimaryIdealsandTheirDifferentialEquations/index.html.
• Related to “Primary decomposition with differential operators”: https://mathrepo.mis.mpg.de/PrimaryDecompositionWithDifferentialOperators/index.html.

Writings

• Syzygies, Postgraduate Diploma Dissertation at The Abdus Salam International Centre for Theoretical Physics.