Joan Elias

Joan Elias

Joan Elias
PhD in mathematics, from Universitat de Barcelona
Professor at Universitat de Barcelona

Personal webpage



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.


Research Interests

  • 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


Selected publications

  • 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.