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.
• A. Iosif. Matemáticas modernas y capitalización del conocimiento matemático en la Educación General Básica Española (2025). Submitted.
• 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 J. Appl. Dyn. Syst. 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 J. Appl. Dyn. Syst. 23(1). arXiv link.
• D. Grigoriev, A. Iosif, H. Rahkooy, T. Sturm, A. Weber. Efficiently and Effectively Recognizing Toricity of Steady State Varieties (2020). Math. Comput. Sci. 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). Bull. Math. Biol. 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. Nolla, R. Muñoz, A. Iosif, L. Ananiadi. Elementary mathematics teacher education programs in Greece, Romania, and Spain (2024). IEJME 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.

• Discriminants à la Sturm for families of affine sections of positive toric varieties. IV Minisimposio Iberoamericano de Álgebra, 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... ¿en el aula de Secundaria? 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

• Ampliación de Matemática Aplicada (Grado en Robótica Software)
• Matemáticas II (Grado en Fundamentos de Arquitectura)

Saint Louis University – Madrid Campus

Seminars

Vademecum

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