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.


    Click here for my full curriculum vitae (March 2021).

    Papers

    Published/In Press
    1. On the Noether bound for noncommutative rings.
             (with E. Kirkman, W. F. Moore and K. Peng), to appear in Proceedings of the AMS.
    2. Semisimple reflection Hopf algebras of dimension sixteen.
             (with E. Kirkman, W. F. Moore and R. Won), to appear in Algebras and Representation Theory.
    3. 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.
    4. Simple $\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension two.
             (with J. Gaddis and R. Won), J. Algebra 562 (2020), 433–465.
    5. 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.
    6. A bimodule structure for the bounded cohomology of commutative local rings.
              J. Algebra 537 (2019), 297–315.
    7. Modules of infinite regularity over commutative graded rings.
             Proc. Amer. Math. Soc. 147 (2019), no. 5, 1929-1939.
    8. Regularity of Tor for weakly stable ideals.
             (with K. Ansaldi and N. Clarke), Le Matematiche 70 N. 1 (2015), 301-310.
    Submitted
  • The InvariantRing package for Macaulay2.
           (with F. Galetto, F. Gandini, H. Huang, M. Mastroeni, X. Ni).
  • Support varieties over skew complete intersections via derived braided Hochschild
            cohomology.
    (with W. F. Moore and J. Pollitz).
    In Preparation
  • A decomposition of the stable cohomology of a local ring.
           (with L. L. Avramov and S. B. Iyengar).
  • The Taylor resolution over a skew polynomial ring.
           (with D. Martin and W. F. Moore).
  • The Eliahou-Kervaire resolution over a skew polynomial ring.
           (with A. Hardesty).
  • The homotopy Lie algebra of a minimal intersection.
           (with M. Gheibi, D. Jorgensen, N. Packauskas and J. Pollitz).
  • On the invariance of homotopy Lie algebras under quasi-isomorphisms.
           (with F. Moore and J. Pollitz).
  • Research with Students

    Research with Graduate Students
  • Alexis Hardesty (TTU). Working on the paper The Eliahou-Kervaire resolution over a skew polynomial ring.
  • Desiree Martin (WFU). Working on the paper The Taylor resolution over a skew polynomial ring.
  • Research with Undergraduate Students
  • Kewen Peng (WFU). Worked on the paper On the Noether bound for noncommutative rings. To appear in Proceedings of the AMS.
  • Macaulay2 Packages

    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).

    Teaching (TTU)

    Undergraduate courses taught as principal instructor:
  • Introduction to Mathematical Reasoning and Proof (MATH 3310) - Summer 2021
  • Higher Mathematics for Engineers and Scientists II (MATH 3351) - Spring 2021
  • 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.