Luca Amata lucamata

I'm a postdoctoral researcher in the department MIFT at University of Messina.

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.