Research

Research Interests

• Applied and Computational Algebra:
  • Applications of commutative algebra, algebraic geometry, and semialgebraic geometry to polynomial ODE systems.
  • Computation and topology of discriminants of semialgebraic systems and positive toric varieties.
  • Algebraic transformations of polynomial ODE systems and their formal algebraic invariants.
• Mathematics Education:
  • Interaction between capitalism and mathematics education (post-modern mathematics curricula).
  • Mathematical formation of teachers.

Research Articles

0. Submitted Articles / Articles in Preparation

• A. Iosif. Duality in mass-action networks (2026). Submitted. arXiv link. Original 2020 manuscript.
• A. Iosif. Discriminants à la Sturm for families of affine sections of positive toric varieties. In Preparation.

A. Applied and Computational Algebra

• A. Desoeuvres, A. Iosif, C. Lüders, O. Radulescu, H. Rahkooy, M. Seiß, T. Sturm. A Computational Approach to Polynomial Conservation Laws (2024). SIAM Journal on Applied Dynamical Systems 23(1). arXiv link.
• A. Desoeuvres, A. Iosif, C. Lüders, O. Radulescu, H. Rahkooy, M. Seiß, T. Sturm. Reduction of Chemical Reaction Networks with Approximate Conservation Laws (2024). SIAM Journal on Applied Dynamical Systems 23(1). arXiv link.
• D. Grigoriev, A. Iosif, H. Rahkooy, T. Sturm, A. Weber. Efficiently and Effectively Recognizing Toricity of Steady State Varieties (2020). Mathematics in Computer Science 15. arXiv link.
• C. Conradi, A. Iosif, and T. Kahle. Multistationarity in the space of total concentrations for systems that admit a monomial parametrization (2019). Bulletin of Mathematica Biololgy 81(10). arXiv link.
• A. Iosif. Algebraic Methods for detecting multistationarity in mass-action networks (2019). PhD Thesis, Otto-von-Guericke-Universität Magdeburg. PDF Link.

B. Mathematics Education

• A. Iosif. Matemáticas modernas y capitalización del conocimiento matemático en la Educación General Básica Española (2026). IXTLI: Revista Latinoamericana de Filosofía de la Educación 13(25).
• A. Nolla, R. Muñoz, A. Iosif, L. Ananiadi. Elementary mathematics teacher education programs in Greece, Romania, and Spain (2024). International Electronic Journal of Mathematics Education 19(4).
• A. Iosif. Elementos de la teoría de conjuntos en la educación secundaria española. Una perspectiva filosófica y socio–crítica (2021). TFM MESOB, UAM.

Other Projects & Documents

• The scalar orbit of the virtual Kähler-Ricci flow.
• Attractors of toric MESSI Systems with no Swap.
• A few aspects of mass-action sheaves.
• Analysis of the Conradi-Kahle algorithm for detecting binomiality on biological models (with H. Rahkooy).
• Maple Discriminant Variety Code.

Talks & Posters

This is a non-exhaustive list of my talks and posters.

• Aplicaciones del álgebra conmutativa y del álgebra real a sistemas de EDOs polinómicas. II Simposio de Investigadores Noveles en Complejidad, Madrid, July 2, 2026.
• Discriminants à la Sturm for families of affine sections of positive toric varieties. IV Minisimposio Iberoamericano de Álgebra, Geometría Algebraica y Singularidades, Tenerife, Jan 30, 2026.
• How toric is Systems Biology? Universidad Complutense de Madrid, June 18, 2025.
• El problema de la multiestacionariedad en sistemas dinámicos con estados estacionarios tóricos. Universidad de La Laguna, Nov 19, 2024.
• Euclid, Descartes, Sturm et al. In search of the real roots of polynomials. Future Algorithms 2024, Online, July 11, 2024. VIDEO
• Duality in mass-action networks: A step closer to a new case of the Global Attractor Conjecture? Congreso RSME 2024, Pamplona, Jan 26, 2024.
• Duality in mass-action networks. ACA 2023, Warsaw, Poland, July 18, 2023.
• The multistationarity problem in dynamical systems with toric steady states. Seminario Matemática Aplicada URJC, March 28, 2023.
• Geometría Algebraica et Ciencia: ¿demasiado álgebra o hacia un nuevo paradigma teórico-computacional? Día Pi, URJC, March 14, 2023.
• Euclides, Descartes y Sturm: la búsqueda de las raíces reales de un polinomio. Seminario Didáctica, UAM, July 15, 2022.
• Using the Tarski-Seidenberg Algorithm to compute the discriminant of a linear section of a positive toric variety. Jíbiri Seminar IV, Zaragoza, June 2022.
• Toric biochemical systems. INRIA Saclay, Paris, Feb 24, 2020.
• Multistationarity in the space of total concentrations... (Poster). SIAM AG, Bern, July 2019.
• Algebraic Methods for the Study of Multistationarity in Mass-Action Networks. (PhD Poster). University of Magdeburg, 2019.

Teaching

Universidad Rey Juan Carlos, Madrid

• Lógica (Grado en Ingeniería Informática)
• Matemática Discreta y Álgebra (Grado en Ingeniería Informática)
• Matemáticas I (Grado en Organización Industrial)

Saint Louis University – Madrid Campus

Seminars

Plazas et caetera

Aquí dejo información útil, entre otras cosas, sobre plazas en Universidades Públicas españolas y portuguesas, poniendo énfasis en las plazas de Ayudante Doctor y las de Professor Auxiliar, así como otros datos de carácter burocrático.