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Achievement: Pull Shark

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lucamata/README.md

I'm a licensed Math teacher (ITIS "E.Torricelli", upper secondary education) with a PhD in Mathematics and Computer Science (University of Catania, 2020).
I had a postdoctoral research experience (University of Messina, 2020-2022) in Computational Algebra and Combinatorics.

📧 luca.amata@scuola.istruzione.it

💻 http://lucamata.github.io

Main interests

  • Hilbert functions and Betti numbers of quotients of exterior algebras
    Characterization of the Hilbert functions of finitely generated modules over an exterior algebra E given the degrees of the possible generators, i.e., of quotients of a fixed free E-module. Moreover, determining of upper bounds for the graded Betti numbers and the graded Bass numbers of such a class of modules via lexicographic submodules.
  • Extremal Betti numbers of some classes of ideals
    Characterization, values as well as positions, of the extremal Betti numbers of strongly stable ideals (also squarefree or t-spread cases). Algorithmic construction of t-spread strongly stable ideal with a given extremal Betti numbers configuration, if possible.
  • Optimal systems of Lie subalgebras
    Looking for efficient algorithms to compute optimal systems of finitely generated Lie subalgebras.
  • Computational algebra
    Developing some packages in CoCoA and Macaulay2 that can be useful in the framework of commutative algebra and algebraic geometry. In particular for deepen the study of the above mentioned topics or approaching some open problems.

Popular repositories Loading

  1. TSpreadIdeals TSpreadIdeals Public

    A Macaulay2 package to deal with t-spread ideals of a polynomial ring. Some details can be found in this paper.

    Macaulay2

  2. lucamata lucamata Public

    Config files for my GitHub profile.

  3. ExteriorModules ExteriorModules Public

    A Macaulay2 package for working with modules over exterior algebra.

    Macaulay2

  4. ExteriorIdeals ExteriorIdeals Public

    A Macaulay2 package for working with ideals over exterior algebra.

    Macaulay2

  5. M2 M2 Public

    Forked from Macaulay2/M2

    The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.

    Macaulay2

  6. GenericInitialModules GenericInitialModules Public

    A Macaulay2 package to compute the generic initial module of a homogeneous module over a polynomial ring.

    Macaulay2