# Dr. Luigi Ferraro

Assistant Professor

School of Mathematical and Statistical Sciences

University of Texas Rio Grande Valley

Assistant Professor

School of Mathematical and Statistical Sciences

University of Texas Rio Grande Valley

Research Mentor: L. Christensen.

Research Mentor: F. Moore.

Advisors: L. Avramov and S. Iyengar.

- Trimming five generated Gorenstein ideals.

(with W. F. Moore). Submitted. - The Improved New Intersection Theorem revisited.

(with L. W. Christensen). To appear in Michigan Mathematical Journal. - The Taylor resolution over a skew polynomial ring.

(with D. Martin and W. F. Moore). To appear in Journal of Algebra and its Applications. - The InvariantRing package for Macaulay2.

(with F. Galetto, F. Gandini, H. Huang, M. Mastroeni, X. Ni). J. Softw. Algebra Geom.**14**(2024),

no. 1, 5-11. - The Eliahou-Kervaire resolution over a skew polynomial ring.

(with A. Hardesty). Comm. Algebra**52**(2024), no. 4, 1636-1655. - The Tor algebra of trimmings of Gorenstein ideals.

(with A. Hardesty). Acta Math. Vietnam.**48**(2023), no. 4, 567-604. - Rigidity of Ext and Tor via flat-cotorsion theory.

(with L. W. Christensen and P. Thompson). Proc. Edinb. Math. Soc. (2)**66**(2023), no. 4,

1142-1153. - The homotopy Lie algebra of a Tor-independent tensor product.

(with M. Gheibi, D. A. Jorgensen, N. Packauskas and J. Pollitz). Illinois J. Math**67**(2023), no. 2,

383-407. - Support varieties over skew complete intersections via derived braided Hochschild

cohomology. (with W. F. Moore and J. Pollitz), J. Algebra**596**(2022), 89-127. - Semisimple reflection Hopf algebras of dimension sixteen.

(with E. Kirkman, W. F. Moore and R. Won), Algebr. Represent. Theory**25**(2022), no. 3, 615-647. - On the Noether bound for noncommutative rings.

(with E. Kirkman, W. F. Moore and K. Peng), Proc. Amer. Math. Soc.**149**(2021), no. 7, 2711–2725. - Differential graded algebra over quotients of skew polynomial rings by normal elements.

(with W. F. Moore), Trans. Amer. Math. Soc.**373**(2020), no. 11, 7755–7784. - Simple $\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension two.

(with J. Gaddis and R. Won), J. Algebra**562**(2020), 433–465. - Three infinite families of reflection Hopf algebras.

(with E. Kirkman, W. F. Moore and R. Won), J. Pure Appl. Algebra**224**(2020), no. 8, 106315. - A bimodule structure for the bounded cohomology of commutative local rings.

J. Algebra**537**(2019), 297–315. - Modules of infinite regularity over commutative graded rings.

Proc. Amer. Math. Soc.**147**(2019), no. 5, 1929-1939. -
Regularity of Tor for weakly stable ideals.

(with K. Ansaldi and N. Clarke), Le Matematiche**70**N. 1 (2015), 301-310.

The Eliahou-Kervaire resolution over a skew polynomial ring. Comm. Algebra

1636-1655.

The Tor algebra of trimmings of Gorenstein ideals. Acta Math. Vietnam.

The Taylor resolution over a skew polynomial ring. To appear in Journal of Algebra and its

Applications.

On the Noether bound for noncommutative rings. Proc. Amer. Math. Soc.

2711–2725.

Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra. Here is a list of packages I co-wrote:

Stable cohomology of local rings and Castelnuovo-Mumford regularity of graded modules.

luigi.ferraro[at]utrgv.edu

EMAGC 3.218, University of Texas Rio Grande Valley, Edinburg, TX.