Dr. Luigi Ferraro

Department of Mathematics
Texas Tech University

Curriculum Vitae

Positions

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 Eliahou-Kervaire resolution over a skew polynomial ring.
           (with A. Hardesty). Submitted.
6. The Taylor resolution over a skew polynomial ring.
           (with D. Martin and W. F. Moore). To appear in Journal of Algebra and its Applications.
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.