Research

Interests

My research interests are in Commutative Algebra with applications to Combinatorics, Discrete Geometry, Algebraic Geometry, Coding Theory or Spline Approximation. Please click this link for a detailed CV. Stuff about me and my research can be also found on Google Scholar and Research Gate. 

Publications

My book: Commutative Algebra Methods for Coding Theory, De Gruyter, 2024. No manuscript is perfect. Here is the open list of corrections for this book: Errata (as of 5/14/2025).

This is the list of my articles. Most of the articles are hyperlinked to their arXiv old versions (hence may contain errors and the exposition is outdated). For the published updated latest versions of the articles, please check the journals’ websites.

1. Betti numbers of fold products of linear forms (with R. Burity)

Submitted; a version is available at arXiv: 2507.07294.

2. Rose-Terao-Yuzvinsky theorem for reduced forms (with R. Burity, Z. Ramos and A. Simis)

J. Algebra 673 (2025), 45-76.

2. Generalized Hamming weights and symbolic powers of Stanley-Reisner ideals of matroids (with M. DiPasquale, L. Fouli and A. Kumar)

Submitted; a version is available at arXiv: 2406.13658.

3. Generalized Hamming weights and minimal shifts of Orlik-Terao algebras

Bull. Math. Soc. Sci. Math. Roumanie, accepted; a version is available at arXiv: 2311.03688.

4. Geometry of the Minimum Distance (with J. Pawlina)

Appl. Algebra Eng. Commun. Comput., to appear, 2024. Click title for open access to published article.

5. On the Jacobian ideal of an almost generic hyperplane arrangement (with R. Burity and A. Simis)

Proc. Amer. Math. Soc. 150 (2022), 4259-4276.

6. Logarithmic derivations associated to line arrangements (with R. Burity)

J. Algebra 581 (2021), 327-352.

7. Homological properties of ideals generated by fold products of linear forms (with R. Burity and Yu Xie)

Michigan Math. J. 74 (2024), 797-824.

8. On Geramita-Harbourne-Migliore conjecture (with Yu Xie)

Trans. Amer. Math. Soc. 374 (2021), 4059-4073.

9. On some ideals with linear free resolution

Unpublished; a version is available at arXiv: 1906.02422.

10. On the containment problem for fat points ideals and Harbourne’s conjecture (with Yu Xie)

Proc. Amer. Math. Soc. 148 (2020), 2411-2419.

11. Generalized minimum distance functions and algebraic invariants of Geramita ideals (with S. Cooper, A. Seceleanu, M. Vaz Pinto and R. Villarreal)

Advances in Applied Math. 112 (2020), 101940.

12. On ideals generated by a-fold products of linear forms

J. Commutative Algebra 13 (2021), 549-570.

13. Equivalent matrices up to permutations (with Jesus Vargas)

Unpublished; a version is available at arXiv: 1805.08343.

14. Free arrangements with low exponents

Extended abstract published in Oberwolfach Reports 5 (2021) 59-61.

15. A blowup algebra for hyperplane arrangements (with M. Garrousian and A. Simis)

Algebra & Number Theory 12 (2018), 1401-1429.

16. Subspace arrangements as generalized star configurations

Mathematische Nachrichten 290 (2017), 3029-3037.

17. Generalized star configurations and the Tutte polynomial (with B. Anzis and M. Garrousian)

J. Algebraic Combinatorics 42 (2017), 165-187.

18. On the geometry of real or complex supersolvable line arrangements (with B. Anzis)

J. Combinatorial Theory, Series A 140 (2016), 76-96.

19. On a conjecture of Vasconcelos via Sylvester forms (with R. Burity and A. Simis)

J. Symbolic Computation 77 (2016), 39-62.

20. Projective duality of arrangements with quadratic logarithmic vector fields

Discrete Mathematics 339 (2016), 54-61.

21. Star Configurations are Set-Theoretic Complete Intersection

Archiv der Mathematik 105 (2015), 343-349.

22. Minimum distance of linear codes and the \alpha-invariant (with M. Garrousian)

Advances in Applied Math. 71 (2015), 190-207.

23. Error-correction of linear codes via colon ideals (with B. Anzis)

J. Algebra (C.S.) 443 (2015), 479-493.

24. The ubiquity of Sylvester forms in almost complete intersections (with A. Simis)

Collectanea Math. 66 (2015), 1-31.

25. Finding inverse systems from coordinates

J. Algebra 400 (2014), 72-77.

26. Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement (with G. Denham and M. Garrousian)

Annals of Combinatorics 18 (2014), 289-312.

27. Homology of homogeneous divisors (with A. Simis)

Israel J. Math. 200 (2014), 449-487.

28. A commutative algebraic approach to the fitting problem

Proc. Amer. Math. Soc. 142 (2014), 659-666.

29. A computational criterion for the supersolvability of line arrangements
    Ars Combinatoria  117 (2014), 217-223.

30. From Splines Approximation to Roth's Equation and Schur Functors (with J. Minac)
    Manuscripta Math. 142(1) (2013), 101-126.

31. On freeness of divisors on P^2
    Communications in Algebra 41(8) (2013), 2916-2932.

32. Growth of the ideal generated by a quadratic multivariate function over GF(3) (with T. Hodges, J. Ding, V. Kruglov, D. Schmidt)
    J. Algebra Appl. 12 (2013), 1250219-1 to 23.

33. Bounding invariants of fat points using a Coding Theory construction (with A. Van Tuyl)
    J. Pure Appl. Algebra 217(2013), 269-279.

34. The minimum distance of sets of points and the minimum socle degree
    J. Pure Appl. Algebra 215(2011), 2645-2651.

35. On the De Boer-Pellikaan method for computing minimum distance
    J. Symbolic Computation 45(2010), 965-974.

36. Lower bounds on minimal distance of evaluation codes
    Appl. Algebra Eng. Commun. Comput. 20(5-6)(2009), 351-360.

37. The Orlik-Terao algebra and 2-formality (with H. Schenck)
    Math. Res. Lett. 16(1)(2009), 171-182.

38. Freeness of Conic-Line Arrangements in P^2 (with H. Schenck)
    Commentarii Mathematici Helvetici 84 (2009) 235-258.

39. Mutant Grobner basis algorithm (with J. Ding, D. Cabarcas, D. Schmidt and J. Buchmann)
    Proceedings of the 1st international conference on Symbolic Computation and Cryptography, Beijing, LMIB, pp. 16-22 (2008).

40. Topological criteria for k-formal arrangements
    Beitrage zur Algebra und Geometrie 48(1)(2007), 27-34.

41. Smooth planar r-splines of degree 2r
    J. Approx. Theory 132(2005), 72-76.