Research

PUBLICATIONS 

• Integrable (3+1)-dimensional generalization for dispersionless Davey--Stewartson system. A. J. Pan-Collantes- Qualitative Theory of Dynamical Systems, 23, 151, 2024. (preprint)

• Integration of Differential Equations by 𝓒∞-structures. A. J. Pan-Collantes, C. Muriel, A. Ruiz- Mathematics, 11(18), 3897, 2023. (preprint)

• 𝒞^∞-structures in the integration of involutive distributions . A. J. Pan-Collantes, A. Ruiz, C. Muriel, J. L. Romero- Physica Scripta, 98(8):085222, 2023. (preprint)

• 𝒞^∞-symmetries of distributions and integrability. A. J. Pan-Collantes, A. Ruiz, C. Muriel, J. L. Romero- Journal of Differential Equations 348(4–5):126, 2023. (preprint)

• On the singular scheme of codimension one holomorphic foliations in ℙ3. L. Giraldo, A. J. Pan-Collantes - International Journal of Mathematics, 2010. (preprint)

PREPRINTS

• Surfaces associated with first-order ODEs.

PhD THESIS

• New methods for the integration of distributions of vector fields.

RESEARCH STAYS

• Slezská univerzita- Matematický ústav. City: Opava,Czech Republic. 10/07/23-10/09/23

• Università Degli Studi Di Milano. City: Milano, Italy. 10/07/22-10/08/22

• IMPA (Instuto Nacional de Matemática Pura e Aplicada de Brasil). City: Angras dos Rei, Brasil. 11/2/2008- 15/2/2008

TALKS

• Surfaces associated with first-order ODEs (slides). Conference: "Advances in Applications of Analytical Methods for Solving Differential Equations (Symmetry 2024)". Nakhon Ratchasima, January 2024.

• Solvable structures and 𝒞^∞-structures (slides). Seminar: "Seminář z diferenciální geometrie a jejich aplikací". Opava, July 2023.

• Integration of differential equations by 𝒞^∞-structures (slides, video). Conference: "Modern Achievements in Symmetries of Differential Equations". Nakhon Ratchasima, December 2022.

• Nuevos métodos de integrabilidad de distribuciones. VIII Jornadas Doctorales del Programa de Doctorado en Matemáticas (UCA). Puerto Real, November 2022.

• ODEs from a geometric point of view (slides). Miniworkshop: "Órbitas en Análisis Matemático". Jerez, September 2021.