His main achivements are the proof of the Sally’s conjectures on the Hilbert fucntion of one-dimensional Cohen-Macualay rings and the characterization of Hilbert polynomials of such rings. He constructed a moduli space of one-dimensional Chen-Macaulay local rings with a given Hilbert polynomial.
- Study and characterization of Hilbert polynomials and functions of local rings
- Homological properties of local rings related with the above problems
- Classification of Artin rings via Macaulay’s inverse systems
- Effectivity of some constructions of local algebra
- Upper bounds of Hilbert coefficients and Hilbert functions. Mathematical Proceedings of the Cambridge Philosophical Society, 2008.
- Isomorphism classes of certain Gorenstein ideals, joint work with G. Valla. Algebras And Representation Theory, 2011.
- Isomorphism classes of short Gorenstein local rings via Macaulay’s inverse system, joint work with M.E. Rossi. Transactions of the American Mathematical Society, 2012.
- On the last Hilbert-Samuel coefficient of isolated singularities, Journal of Algebra, 2013.
- Analytic isomorphism of compressed local algebras, joint work with M.E. Rossi. Proceedings of the American Mathematical Society,2015.