Institutos Universitarios

Patricio Almirón Cuadros

Personal de apoyo a la investigación (Predoctoral Fellow)
Department of Algebra, geometry and topology
School of Mathematical Sciences
Complutense University of Madrid
Grupo Singular
Spanish Network of Algebraic Geometry and Singularities (RGAS)



I am a PhD student in mathematics at Complutense University of Madrid. My advisors are María Alberich-Carramiñana  and Alejandro Melle-Hernández. In 2019, I have done a 1 month research stay at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, México, and a 2 and half months research stay at Technische Universität Kaiserslautern in Kaiserslautern, Germany. My main interests are about singularities of curves, using techniques of algebraic geometry, commutative algebra and topology and also numerical semigroups. I focus my study in two areas: analytic invariants of planar curves and morphisms and numerical semigroups and its combinatorics.

I also like dissemination of science. I collaborate with the radio program El zoo de Schrödinger at Inforadio Ucm. In addition, I am one of the founding members of the project Cometas of dissemination of mathematics at the Faculty of Mathematics in Complutense University of Madrid.


Research interests

Algebra, geometry and topology. Deformations of isolated singularities. Analytic and topological invariants of isolated singularities. 


Latest Publications

  •  P. Almirón, On the quotient of Milnor and Tjurina numbers for two-dimensional isolated hypersurface singularities. Mathematische Nachrichten, 2022, pp. 1–10.
  •  P. Almirón,  J. J. Moyano-Fernández, Supersymmetric gaps a numerical semigroup with two generators. Communications in Algebra, 2022, volumen 50,  issue 10, pp. 4252-4268.
  • P. Almirón, M. Schulze, Limit spectral distribution for non-degenerate hypersurface singularities.Comptes Rendus. Mathématique, 2022, 360, pp. 699-710.22222.
  • P. Almirón, J.J Moyano-Fernández. Eliahou number, Wilf function and concentration of a numerical semigroup, Quaestiones Mathematicae, 2022, DOI: 10.2989/16073606.2022.2041126
  • P. Almirón. The 4/3 problem for germs of isolated plane curve singularities. In Extended Abstracts GEOMVAP 2019. Birkhäuser. Trends in Mathematics. 2021, 15, 139-143.
  • P. Almirón, J. J. Moyano-Fernández. A formula for the conductor of a semimodule of a numerical semigroup with two generators. Semigroup Forum. 2021, 103, 278–285.
  • M. Alberich-Carramiñana, P. Almirón, G. Blanco, A. Melle-Hernández. The minimal Tjurina number of irreducible germs of plane curve singularities. Indiana University Mathematics Journal. 2021, 70, 4, 1211–1220.