# Dr. Luigi Ferraro

Department of Mathematics
Texas Tech University

## Curriculum Vitae

##### Positions
• Fall 2020 - Present: Postdoc at Texas Tech University.
Research Mentor: L. Christensen.
• Fall 2017 - Summer 2020: Postdoc at Wake Forest University.
Research Mentor: F. Moore.
• Fall 2011 - Summer 2017: Graduate Teaching Assistant at the University of Nebraska-Lincoln.
Advisors: L. Avramov and S. Iyengar.
• ##### Research Interests

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.

## Papers and Preprints

1. The Improved New Intersection Theorem revisited.
(with L. W. Christensen). Submitted.
2. The Tor algebra of trimmings of Gorenstein ideals.
(with A. Hardesty). Submitted.
3. Rigidity of Ext and Tor via flat-cotorsion theory.
(with L. W. Christensen and P. Thompson). Submitted.
4. The homotopy Lie algebra of a Tor-independent tensor product.
(with M. Gheibi, D. A. Jorgensen, N. Packauskas and J. Pollitz). Submitted.
5. The Taylor resolution over a skew polynomial ring.
(with D. Martin and W. F. Moore). Submitted.
6. The Eliahou-Kervaire resolution over a skew polynomial ring.
(with A. Hardesty). Submitted.
7. 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.
8. Support varieties over skew complete intersections via derived braided Hochschild
cohomology.
(with W. F. Moore and J. Pollitz), J. Algebra 596 (2022), 89-127.
9. 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.
10. 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.
11. 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.
12. Simple $\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension two.
(with J. Gaddis and R. Won), J. Algebra 562 (2020), 433–465.
13. 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.
14. A bimodule structure for the bounded cohomology of commutative local rings.
J. Algebra 537 (2019), 297–315.
15. Modules of infinite regularity over commutative graded rings.
Proc. Amer. Math. Soc. 147 (2019), no. 5, 1929-1939.
16. Regularity of Tor for weakly stable ideals.
(with K. Ansaldi and N. Clarke), Le Matematiche 70 N. 1 (2015), 301-310.

## Research with Students

• Alexis Hardesty (TTU). The Tor algebra of trimmings of Gorenstein ideals. Submitted.
• Alexis Hardesty (TTU). The Eliahou-Kervaire resolution over a skew polynomial ring. Submitted.
• Desiree Martin (WFU). The Taylor resolution over a skew polynomial ring. Submitted.
• ##### Research with Undergraduate Students
• Kewen Peng (WFU). On the Noether bound for noncommutative rings. Proc. Amer. Math. Soc.
149 (2021), no. 7, 2711–2725.
• ## Software

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

• InvariantRing,
•        (with F. Galetto, F. Gandini, H. Huang, T. Hawes, M. Mastroeni and X. Ni).
• ResLengthThree,
•        (with L. W. Christensen, F. Gandini, F. Moore and O. Veliche).

## Seminars

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 I1=(x2,xy),I2=(y2) be ideals of R. Set S1=R/I1, S2=R/I2 and S=R/(I1+I2). Then $\pi$(S) is a free Lie algebra since the square of the maximal ideal of $S$ is zero. While $\pi$(S1)$\times$$\pi$(R)$\pi$(S2) is not free because an element of degree 2 of $\pi$(S1) commutes with an element of degree 2 of $\pi$(S2); this follows from the fact that R is regular and so $\pi$(R) is concentrated in degree 1.

## Teaching (TTU)

##### Undergraduate courses taught as principal instructor:
• Differential Equations II (MATH 4354) - Summer 2022
• Higher Mathematics for Engineers and Scientists I (MATH 3350) - Spring 2022, Summer 2022
• Calculus III with Applications (MATH 2459) - Fall 2021
• Introduction to Mathematical Reasoning and Proof (MATH 3310) - Summer 2021
• Higher Mathematics for Engineers and Scientists II (MATH 3351) - Spring 2021, Spring 2022
• Differential Equations I (MATH 3354) - Spring 2021
• Calculus II with Applications (MATH 1452) - Fall 2020
• ##### Online graduate certificate courses taught as principal instructor:
• Abstract Algebra Applied I (MATH 5368) - Fall 2020
• ## Teaching (WFU)

##### Graduate courses taught as principal instructor:
• Abstract Algebra II (MST 722) - Spring 2019
• Abstract Algebra I (MST 721) - Fall 2018
• ##### Undergraduate courses taught as principal instructor:
• Elementary Probability and Statistics (STA 111) - Summer 2020
• Linear Algebra II (MST 225) - Spring 2020
• Multivariable Calculus (MST 113) - Fall 2019, Spring 2020, Summer 2020
• Ordinary Differential Equations (MST 251) - Summer 2018, 2019 and Fall 2018, 2019
• Calculus with Analytic Geometry II (MST 112) - Summer 2018, Spring 2019
• Modern Algebra I (MST 321) - Spring 2018
• Linear Algebra I (MST 121) - Spring 2018, Summer 2019
• Calculus with Analytic Geometry I (MST 111) - Fall 2017
• ## Teaching (UNL)

##### Undergraduate courses taught as principal instructor:
• Differential Equations (Math 221) - Spring 2016, Spring 2017, Summer 2017
• College Algebra and Trigonometry (Math 103) - Fall 2015, Fall 2016
• Contemporary Mathematics (Math 203) - Fall 2014
• ##### Recitations
• Analytic Geometry and Calculus II (Math 107) - Fall 2013, Spring 2014
• Analytic Geometry and Calculus I (Math 106) - Fall 2012, Spring 2013
• ## Contacts

lferraro[at]ttu.edu
348 Weeks Hall, Texas Tech University, Lubbock, TX.