Research

My research interests lie in Algebraic Geometry, Commutative Algebra, and Combinatorics.

Papers

1. Irrational components of the Hilbert scheme of points (with G. Farkas, R. Pandharipande), submitted.

2. On minimal presentations of numerical monoids (with A. Moscariello), submitted.

3. Open problems on relations of numerical semigroups (with A. Moscariello), submitted.

4. The geometry of double nested Hilbert schemes of points on curves (with M. Graffeo, P. Lella, S. Monavari, A. T. Ricolfi), pending revision.

5. Bounds for syzygies of monomial curves (with G. Caviglia, A. Moscariello), Proceedings of the American Mathematical Society, to appear.

6. Higher resonance schemes and Koszul modules of simplicial complexes (with M. Aprodu, G. Farkas, C. Raicu, A. Suciu), Journal of Algebraic Combinatorics, in press (available online).

7. On the parity conjecture for Hilbert schemes of points on threefolds (with R. Ramkumar), Annali della Scuola Normale Superiori di Pisa, Classe di Scienze, in press (available online).

8. Rational singularities of nested Hilbert schemes (with R. Ramkumar), International Mathematics Research Notices 2024, 1061-1122 (2024).

9. On Rees algebras of 2-determinantal ideals (with R. Ramkumar), Journal of the London Mathematical Society 109, e12821 (2024).

10. Syzygies in Hilbert schemes of complete intersections (with G. Caviglia), Journal of Algebra 619, 538-557 (2023).

11. On the tangent space to the Hilbert scheme of points in P3 (with R. Ramkumar), Transactions of the American Mathematical Society 375, 6179-6203 (2022).

12. On the smoothness of lexicographic points on Hilbert schemes (with R. Ramkumar), Journal of Pure and Applied Algebra 226, (2022).

13. Relations between the 2x2 minors of a generic matrix (with M. Perlman, H. Huang, C. Polini, C. Raicu), Advances in Mathematics 386, (2021).

14. Blowup algebras of rational normal scrolls, Transactions of the American Mathematical Society 373, 797-818 (2020).

15. On the multiplicity of tangent cones of monomial curves, Arkiv för Matematik 57, 215-225 (2019). 

16. Correspondence scrolls (with D. Eisenbud), Acta Mathematica Vietnamica 44, 101-116 (2019). 

17. On the Lex-plus-powers conjecture (with G. Caviglia), Advances in Mathematics 340, 284-299 (2018).

18. On the growth of deviations (with A. Boocher, A. D'Alì, E. Grifo, J. Montaño), Proceedings of the American Mathematical Society 144, 5049-5060 (2016).

19. Consecutive cancellations in Tor modules over local rings, Journal of Pure and Applied Algebra 220, 3861-3865 (2016).

20. s-Hankel hypermatrices and 2 x 2 determinantal ideals, Journal of Commutative Algebra 8, 239-273 (2016).

21. Edge ideals and DG algebra resolutions (with A. Boocher, A. D'Alì, E. Grifo, J. Montaño), Le Matematiche 70, 215-237 (2015).

22. On a conjecture by Wilf about the Frobenius number (with A. Moscariello), Mathematische Zeitschrift 280, 47-53 (2015).

23. Classes of complete intersection numerical semigroups (with M. D'Anna, V. Micale), Semigroup Forum 88, 453-467 (2014).

24. When the associated graded ring of a semigroup ring is complete intersection (with M. D'Anna, V. Micale), Journal of Pure and Applied Algebra 217, 1007-1017 (2013).

25. Numerical semigroups with large embedding dimension satisfy Wilf's conjecture, Semigroup Forum 85, 439-447 (2012).

26. On the associated graded ring of a semigroup ring (with M. D'Anna and V. Micale), Journal of Commutative Algebra 3, 147-168 (2011).