# 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.

- Rigidity of Ext and Tor via flat-cotorsion theory.

(with L. 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 Taylor resolution over a skew polynomial ring.

(with D. Martin and W. F. Moore). Submitted. - The Eliahou-Kervaire resolution over a skew polynomial ring.

(with A. Hardesty). Submitted. - The InvariantRing package for Macaulay2.

(with F. Galetto, F. Gandini, H. Huang, M. Mastroeni, X. Ni). Submitted. - Support varieties over skew complete intersections via derived braided Hochschild

cohomology. (with W. F. Moore and J. Pollitz), to appear in Journal of Algebra. - Semisimple reflection Hopf algebras of dimension sixteen.

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

polynomial ring. Submitted.

Submitted.

Proc. Amer. Math. Soc.

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.

CHAMP is a weekly online seminar series; its main goal is to give graduate students and other early career researchers on the job market a platform to give a 50 minutes talk about their research. This is the seminar that I gave at CHAMP, based on my paper The homotopy Lie algebra of a Tor-independent tensor product.

Here is a counterexample answering the question that Eloisa asked at the end of the talk: let k be a field, let R=k[[x,y]] be a power series ring and let I_{1}=(x^{2},xy),I_{2}=(y^{2}) be ideals of R. Set S_{1}=R/I_{1}, S_{2}=R/I_{2} and S=R/(I_{1}+I_{2}). Then $\pi$(S) is a free Lie algebra since the square of the maximal ideal of $S$ is zero. While
$\pi$(S_{1})$\times$_{$\pi$(R)}$\pi$(S_{2}) is not free because an element of degree 2 of $\pi$(S_{1}) commutes with an element of degree 2 of $\pi$(S_{2}); this follows from the fact that R is regular and so $\pi$(R) is concentrated in degree 1.

lferraro[at]ttu.edu

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