Articles (published/accepted)

• Understanding Surgical smoke in Laparoscopy through Lagrangian Coherent Structures  (with C. Crowley, M. F. Khan, M. D. Bustamante, R. Cahill and K. Nolan), PLoS ONE 18(11): e0293287  2023, DOI:10.1371/journal.pone.0293287 .

• The Frisch--Parisi formalism for fluctuations of the Schrödinger equation (with F. Ponce-Vanegas, L. Roncal and L. Vega), to appear in the Springer Proceedings of Mathematics and Statistics. Preprint arXiv:2202.06645. 

• Static and Dynamical, Fractional Uncertainty Principles (with F. Ponce-Vanegas and L. Vega),  Transactions of the Americal Mathematical Society, vol. 375, no. 8, pp. 5691–5725, 2022, DOI: 10.1090/tran/8655 Preprint arXiv:2103.03794. 

• On the Schrödinger map for regular helical polygons in the hyperbolic space, Nonlinearity, vol. 35, no. 1, pp. 84–109, 2022, DOI:10.1088/1361-6544/ac355c Preprint arXiv:2010.12045.

•  Vortex Filament Equation for a regular polygon in the hyperbolic plane (with F. de la Hoz and L. Vega),  Journal of Nonlinear Science, vol. 32, no. 9, 2022, DOI: 10.1007/s00332-021-09757-7, Preprint arXiv:2007.04944.

• Recent progress on the vortex filament equation for regular polygons. TEMatmonográficos, 2 (2021): Proceedings of the 3rd BYMAT Conference, pp. 235–238, ISSN: 2660-6003.

• Safe trajectory of a piece moved by a robot, Applications of Industrial Mathematics, RSME Springer Series, vol. 8, pp. 31--52, ebook ISBN: 978-3-031-32130-6. 

•  On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion (with F. de la Hoz and L. Vega), SIAM Journal on Applied Mathematics, vol. 80, no. 2, pp. 1034–1056, 2020, DOI:10.1137/19M1272755,  arXiv:1909.01029.

• Vortex Filament Equation for a regular polygon in the Hyperbolic plane (with F. de la Hoz and L. Vega), Proceedings of the CEDYA + CMA 2017, Cartagena (Spain), 2017, pp. 379–384, ISBN 978-84-944402-1-2.

Preprints

• Pseudorandomness of the Schrödinger map equation, Preprint arXiv:2311.01611, 2023.

• On Lagrangian Coherent Structures in Laparoscopy (with C. Crowley, M. F. Khan, M. D. Bustamante, R. Cahill and K. Nolan), Preprint arXiv:2212.12763. 

Theses 

• Vortex Filament Equation for some Regular Polygonal Curves (PhD thesis). 

• Mathematical models and numerical methods for Reaction-Diffusion problems in composite media (Master thesis).