# Dr. Luigi Ferraro

Department of Mathematics

Texas Tech University

Department of Mathematics

Texas Tech University

Research Mentor: L. Christensen.

Research Mentor: F. Moore.

Advisors: L. Avramov and S. Iyengar.

One of my research interests is in commutative algebra, in particular in the use of homological tools to study commutative rings. I am also interested in non-commutative algebra, in particular in the actions of Hopf algebras on rings and the homological properties of quotients of skew polynomial rings.

- The Improved New Intersection Theorem revisited.

(with L. W. Christensen). Submitted. - The Tor algebra of trimmings of Gorenstein ideals.

(with A. Hardesty). Submitted. - Rigidity of Ext and Tor via flat-cotorsion theory.

(with L. W. Christensen and P. Thompson). Submitted. - The homotopy Lie algebra of a Tor-independent tensor product.

(with M. Gheibi, D. A. Jorgensen, N. Packauskas and J. Pollitz). Submitted. - The Eliahou-Kervaire resolution over a skew polynomial ring.

(with A. Hardesty). Submitted. - 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). To appear in Journal of Software for

Algebra and Geometry. - 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.

Algebra and its Applications.

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.

The main goal of CHAMPS is to give graduate students and other early career researchers on the academic job market a platform to showcase their research. Find below my CHAMPS elevator pitch, where I briefly explain my work experience and my research.

lferraro[at]ttu.edu

348 Weeks Hall, Texas Tech University, Lubbock, TX.