# 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.

- On the Noether bound for noncommutative rings.

(with E. Kirkman, W. F. Moore and K. Peng), to appear in Proceedings of the AMS. - Semisimple reflection Hopf algebras of dimension sixteen.

(with E. Kirkman, W. F. Moore and R. Won), to appear in Algebras and Representation Theory. - 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.

(with F. Galetto, F. Gandini, H. Huang, M. Mastroeni, X. Ni).

cohomology. (with W. F. Moore and J. Pollitz).

(with L. L. Avramov and S. B. Iyengar).

(with D. Martin and W. F. Moore).

(with A. Hardesty).

(with M. Gheibi, D. Jorgensen, N. Packauskas and J. Pollitz).

(with F. Moore and J. Pollitz).

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.

lferraro[at]ttu.edu

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