Dr. Luigi Ferraro

Assistant Professor
School of Mathematical and Statistical Sciences
University of Texas Rio Grande Valley

Curriculum Vitae

Positions
  • Fall 2023 - present: Assistant Professor at the University of Texas Rio Grande Valley.
  • Fall 2020 - Summer 2023: 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

  • Commutative Algebra. My research has focused on the structure of the stable cohomology of a local ring, on the Castelnuovo-Mumford regularity of graded modules, on the rigidity of Ext and Tor, on the intersection theorems, on grade 3 perfect ideals and on the homotopy Lie algebra of local rings.
  • Noncommutative Algebra. My research has focused on studying actions of groups and, more generally, actions of Hopf algebras on noncommutative rings. My research has also focused on the study of the homological properties of quotients of skew polyomial rings by ideals generated by normal elements, through the use of DG algebra resolutions.

  • Click here for my full curriculum vitae (February 2024).

    Papers and Preprints

    1. The Eliahou-Kervaire resolution over a skew polynomial ring.
              (with A. Hardesty). To appear in Communications in Algebra.
    2. The Tor algebra of trimmings of Gorenstein ideals.
              (with A. Hardesty). To appear in Acta Mathematica Vietnamica.
    3. Rigidity of Ext and Tor via flat-cotorsion theory.
              (with L. W. Christensen and P. Thompson). To appear in Proceedings of the Edinburgh
              Mathematical Society .
    4. The Improved New Intersection Theorem revisited.
              (with L. W. Christensen). To appear in Michigan Mathematical Journal.
    5. The Taylor resolution over a skew polynomial ring.
              (with D. Martin and W. F. Moore). To appear in Journal of Algebra and its Applications.
    6. 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.
    7. The homotopy Lie algebra of a Tor-independent tensor product.
              (with M. Gheibi, D. A. Jorgensen, N. Packauskas and J. Pollitz). Illinois J. Math 67 (2023), no. 2,
              383-407.
    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

    Research with PhD Students
  • Alexis Hardesty (TTU).
            The Eliahou-Kervaire resolution over a skew polynomial ring. To appear in Communications in
            Algebra.
            The Tor algebra of trimmings of Gorenstein ideals. To appear in Acta Mathematica Vietnamica.
  • Research with Master's Students
  • Raul Alvarez (UTRGV).
  • Desiree Martin (WFU).
            The Taylor resolution over a skew polynomial ring. To appear in Journal of Algebra and its
            Applications.
  • 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).

    Teaching (UTRGV)

    Graduate courses taught as principal instructor:
  • Algebra II (MATH 6632) - Spring 2024
    Undergraduate courses taught as principal instructor:
  • Applied Discrete Mathematics (MATH 3361) - Fall 2023
  • Teaching (TTU)

    Undergraduate courses taught as principal instructor:
  • Advanced Calculus I (MATH 4350) - Summer 2023
  • 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, Fall 2022
  • 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, Spring 2023
  • 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

      luigi.ferraro[at]utrgv.edu
      EMAGC 3.218, University of Texas Rio Grande Valley, Edinburg, TX.