Research  Lines

My research focuses in the areas of Ordinary and Partial Differential Equations, Nonlinear Analysis, Dynamical Systems and Mathematical modelling. The main results obtained so far in these areas are:

• General elliptic systems: analysis of existence, uniqueness and multiplicity through local and global bifurcation methods of componentwise positive solutions for general second order elliptic systems with applications to classical and Holling-Tanner predator-prey models. 

• Classical ODE predator-prey model: global characterization of the existence of periodic solutions for the classical periodic Volterra predator-prey model via bifurcation and nonlinear analysis techniques.

• Hamiltonian systems: analysis of existence and multiplicity of periodic solutions and subharmonics in planar Hamiltonian systems with general weights via topological methods as the Poincaré-Birkhoff fixed point theorem, Conley-Zehnder index and shooting techniques. Study of complex and chaotic dynamics through the topological horseshoes theory.

Some invited Talks and Seminars

• January 2026: Bienal RSME 2026, Alicante, Spain

• May 2025: Seminar at Waseda University, Tokyo, Japan

• March 2025: Periodic DEG1 Meeting, Trieste, Italy

• January 2025: RSME's VII Congress of Young Researchers, Bilbao, Spain

• October 2024: Nonlinear PDE, Madrid, Spain

• September 2024: Nonlinear Meeting in Reggio Emilia, Reggio Emilia, Italy

• July 2024: ECM Congress, Sevilla, Spain

• June 2024: CEDYA XXVIII, Bilbao, Spain 

• May 2024: Seminario Matematico PoliMi, Milano, Italy

• April 2024: EELISA Connect Workshop, Madrid, Spain

• September 2023: DEDA 2023, Alba, Italy

• July 2023: Seminario Matematico UniMoRe, RE, Italy

• June 2023: 13th AIMS Conference, Wilmington, NC, USA

• February 2023: RSME Young Researchers, León, Spain

• November 2022: Seminar UAM-ICMAT, Madrid, Spain

• July 2022: CEDYA XXVII, Zaragoza, Spain

• July 2022: EquaDiff 15, Brno, Czech Republic

• June 2022: Seminario Matematico UniFi, Firenze, Italy

• June 2022: Nonlinear Afternoon, Udine, Italy

• June 2022: Seminario Matematico U. Trieste, Trieste, Italy

• June 2021: Seminario Matematico UniTo, Torino, Italy

• June 2021: Society Mathematical Biology, Online Meeting

Seminars Coordinator

• September 2025-present: Department of Mathematical Analysis and Applied Mathematics Seminar UCM, with María Jesús Carro

• 2020-2022: PhD Math Seminar UCM, with Jesús Llorente Jorge