About me


I specialize in Commutative Algebra and its applications to Algebraic Geometry. I am interested on local cohomology, Lyubeznik numbers, and D-modules over all characteristics (zero, prime and mixed). I also work on methods in positive characteristic; in particular, on F-modules, F-thresholds, tight closure, and test ideals. I am also interested in homological invariants, such as projective dimension and Castelnuovo-Mumford regularity. Lately, I have been studying binomal edge ideals and their interactions with graph theory. I am also recently interested in symbolic powers. My research is partially supported by CONACYT Ciencia Básica Grant #284598. Before moving to CIMAT, my research was partially supported by NSF Grant DMS 1502282.

Publication list:

1. "Ideals with Larger Projective Dimension and Regularity" (with Jesse Beder, Jason McCullough, Alexandra Seceleanu, Bart Snapp and Branden Stone), Journal of Symbolic Computation, Vol. 46 (2011), No. 10, 1105-1113.

2. "Local cohomology properties of direct summands", Journal of Pure Applied and  Algebra, Vol. 216 (2012) No. 10, 2137-2140.

3. "On certain rings of differentiable type and finiteness properties of local cohomology", Journal of Algebra, Vol. 379 (2013), 1-10.

4. Local cohomology modules of polynomial or power series rings over rings of small dimension", Illinois Journal of Mathematics, Vol. 57 (2013), No. 1, 279-294.

5. "Lyubeznik numbers in mixed characteristic" (with Emily E. Witt), Mathematical Research Letters, Volume 20 (2013), No. 6, 1125-1143.

6. "Associated primes of local cohomology of flat extensions with regular fibers and Σ-finite D-modules", Journal of Algebra, Vol. 399 (2014), 770-781.

7. "Generalized Lyubeznik numbers" (with Emily E. Witt), Nagoya Journal of Mathematics, Vol. 215 (2014), 168-202.

8. "Properties of Lyubeznik numbers under localization and polarization'' (with Arindam Banerjee and Kohji Yanagawa), Journal of Pure and Applied Algebra, Vol. 219 (2015), No. 11, 4872-4888.

9. "F-jumping and F-Jacobian ideals for hypersurfaces" (with Felipe Pérez), Journal Pure and Applied Algebra, Vol. 220 (2016), No. 1, 292-318.

10. "A sufficient condition for strong F-regularity" (with Alessandro De Stefani), Proceedings of the American Mathematical Society, Vol. 144 (2016), No. 1, 21-29.

11. "A survey on the Lyubeznik numbers" (with Emily E. Witt and Wenliang Zhang), Contemporary Mathematics, Vol. 657 (2016), 154-181.

12. "F-pure thresholds of quasi-homogeneous polynomials" (with Daniel J. Hernández, Emily E. Witt and Wenliang Zhang), Michigan Mathematical Journal, Vol. 65 (2016), No. 1, 57-87.

13. "Frobenius Betti numbers and modules of finite projective dimension" (with Alessandro De Stefani and Craig Huneke), Journal of Commutative Algebra, Vol. 9 (2017), No. 4, 455-490.

14. "On the hyperhomology of the small gobelin for codimension 2" (with Xavier Gómez-Mont), Boletín de la Sociedad Matemática Mexicana, Vol. 23 (2017), No. 2, 623-651.

15. "Binomial edge ideal and graph connectivity" (with Arindam Banerjee), Proceedings of the American Mathematical Society, 145 (2017), No. 2, 487–499.

16. "F-thresholds of graded rings'' (with Alessandro De Stefani), Nagoya Journal of Mathematics, Vol. 229 (2018), 141-168.

17. "Local m-adic constancy of F-pure thresholds and test ideals for hypersurfaces with isolated singularities'', (with Daniel J. Hernández and Emily E. Witt), Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 164 (2018), No. 2, 285-295.

18. "On the support of local cohomology via Frobenius'' (with Mel Hochster), Mathematical Research Letters}, Vol. 24 (2017), No. 2, 40-420.

19. "Footprint and minimum distance functions" (with Yuriko Pitones and Rafael Heraclio Villarreal), Communications of the Korean Mathematical Society, Vol. 33 (2018), No. 1, 85-101.

20. "D-modules, Bernstein-Sato polynomials, and F-invariants of direct summands'' (with Josep Àlvarez-Montaner and Craig Huneke), Advances in Mathematics, Vol. 321 (2017), 298-325.

21. "On the existence of F-thresholds and related limits'' (with Alessandro De Stefani and Felipe Pérez), Transactions of the American Mathematical Society, Vol. 370 (2018), No. 9, 6629-6650.

22. "Symbolic powers of ideals" (with Hailong Dao, Alessandro De Stefani, Craig Huneke and Eloísa Pires), Singularities and foliations. geometry, topology and applications, 387-432, Springer Proc. Math. Stat., Vol. 222 (2018), Springer, Cham.

23. "Lyubeznik numbers and injective dimension of local cohomology modules''
(with Daniel J. Hernández, Felipe Pérez and Emily E. Witt), Transactions of the American Mathematical Society. Vol 371 (2019), No. 11, 7533-7557.

24. "Cohomological dimension, Lyubeznik numbers, and connectivity in mixed characteristic'' (con Daniel J. Hernández, Felipe Pérez and Emily E. Witt), Journal of Algebra, Vol. 514 (2018), 442–467.

25. "Connectedness and Lyubeznik numbers" (with Sandra Spiroff y Emily E. Witt), 2019, no. 13, 4233–4259..

26. "Local cohomology and Lyubeznik numbers of F-pure rings" (with Alessandro De Stefani, and Eloísa Pires), to appear Journal of Algebra.

27. "Hilbert-Kunz multiplicities and F-thresholds'' (con Ilya Smirnov), to appear en Boletín de la Sociedad Matemática Mexicana.

28. "On the symbolic square-free monomial ideals" (con Jonathan Montaño), to appear en International Mathematical Research Notices.

29. "Quantifying singularities with differetial operators" (with Holger Brenner and Jack Jeffries), to apper in Advances in Mathematics.

30. "b-vectors of chordal graphs" (con Luis Pedro Montejano), sometido.

31. "Functional equations, V-filtrations and multiplier ideals of direct summands" (con Josep álvarez-Montaner, Daniel J. Hernández, Jack Jeffires, Pedro Teixeira, and Emily E. Witt), en preparación.