Research

My main research interests lie in commutative algebra and algebraic geometry. I am primary interest is in questions that arise in geometrical or combinatorial contexts and try to understand how their possible answers manifest in various algebraic structures or invariants. I often collaborate on problems at the interface of commutative algebra, algebraic geometry, and combinatorics. I like topics related to blow-up algebras, local cohomology, multiplicities, differential operators, integral closure, Hilbert schemes, symbolic powers, syzygies, regularity, and matroids.

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 Federico Castillo, Binglin Li, Jonathan Montaño and Naizhen Zhang), When are multidegrees positive?,
    FPSAC 2021 Proceedings, Séminaire Lotharingien de Combinatoire 85B (2021), Art. 46, 12 pp, journal version.
15. (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.
16. (with Jonathan Montaño), Mixed mulitplicities of graded families of ideals,
    Journal of Algebra 590 (2022) 394–412, journal version, arXiv:2010.11862.
17. Equations and multidegrees for inverse symmetric matrix pairs,
    Le Matematiche Vol. LXXVI (2021) - Issue II, pp. 369–381, journal version, arXiv:2011.04616.
18. (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.
19. (with Bernd Sturmfels), Primary decomposition with differential operators,
    International Mathematics Research Notices, rnac178, 2022, journal version, arXiv:2101.03643.
20. (with Justin Chen), Primary decomposition of modules: a computational differential approach,
    Journal of Pure and Applied Algebra 226, 2022, journal version, arXiv:2104.03385.
21. (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.
22. Fiber-full modules and a local freeness criterion for local cohomology modules,
    Mathematische Zeitschrift 303, 30 (2023), journal version, arXiv:2106.07777.
23. (with Ritvik Ramkumar), The fiber-full scheme,
    Journal of Pure and Applied Algebra, journal version, arXiv:2108.13986.
24. (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.
25. (with Oliver Clarke and Fatemeh Mohammadi), A study of nonlinear multiview varieties,
    Journal of Algebra 620 (2023) 363–391, journal version, arXiv:2112.06216.
26. (with Ritvik Ramkumar), A local study of the fiber-full scheme,
    Journal of Algebra 636 (2023) 248–278, journal version, arXiv:2202.06652.
27. (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), journal version, arXiv:2205.03837.
28. (with Alessio Caminata and Aldo Conca), Multidegrees, prime ideals, and non-standard gradings,
    Advances in Mathematics 435 (2023) 109361, journal version, arXiv:2208.07238.
29. (with Federico Castillo, Fatemeh Mohammadi and Jonathan Montaño), K-polynomials of multiplicity-free varieties, arXiv:2212.13091.
30. (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.
31. Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities, arXiv:2311.15105.
32. Polar multiplicities and integral dependence,
    International Mathematics Research Notices 2024, 00(0), 1–18, journal version, arXiv:2401.10198.
33. (with Jack Jeffries), Uniformity in nonreduced rings via Noetherian operators,
    International Mathematics Research Notices Vol 2025, Issue 17, Sep 2025, journal version, arXiv:2404.02057.
34. (with Claudia Polini and Bernd Ulrich), Multidegrees, families, and integral dependence, arXiv:2405.07000.
35. (with Yupeng Li and Jacob P. Matherne), Log-concavity of polynomials arising from equivariant cohomology, arXiv:2411.17572.
36. (with Yupeng Li and Jacob P. Matherne), Log-concavity of polynomials arising from equivariant cohomology,
    FPSAC 2025 Proceedings, Séminaire Lotharingien de Combinatoire 93B (2025) Art. 68, 12 pp, journal version.
37. Mixed Segre zeta functions and their log-concavity, arXiv:2507.06424.
38. (with Jacob P. Matherne and Anna Shapiro), Syzygies of polymatroidal ideals, arXiv:2507.13153.

Teaching

Notes

• Graded Moebius algebras and the cohomology ring of matroid Schubert varieties
• Syzygies, Postgraduate Diploma Dissertation at The Abdus Salam International Centre for Theoretical Physics

Macaulay2 codes & resources

• Mixed Segre zeta functions: mixed_Segre.m2
• Package for multi‑graded rational maps: MultiGradedRationalMap.m2 + examples
• Primary ideals & their differential equations: MathRepo MPI Leipzig
• Primary decomposition with differential operators: MathRepo MPI Leipzig

Contact