Esteban Paduro

Since 2021 postdoc at Pontificia Universidad Católica de Chile

Funded by ANID FONDECYT postdoctoral.

email: esteban.paduro (at) gmail

Google Scholar profile

Current Reseach

Conduction Block in Neurostimulation: In neuroscience, reversible conduction block refers to a mechanism by which, via the application of a high-frequency input, an action potential generated on one end of the axon cannot reach the other end. The reversibility stems from the fact that the external stimulus is not strong enough to permanently damage the tissue, and that after the external signal is removed, the neuron returns to its original state. We study reversible conduction block from the perspective of the failure of signal propagation in an axon model.
Prediction in Spatial Statistics based on the SPDE approach.

Research interests

Neurostimulation: Currently interested in understanding the responses of neuron systems to electrical stimulation. Particularly recently I have been working on the problems of conduction block and interferential current stimulation.

Fluid Mechanics: I am interested in the question of the loss of well-posedness happening on fluid equations when the regularity of the initial data is not enough. In my PhD thesis, I considered an explicit construction of initial data that made the solutions arbitrarily large after an arbitrarily short time.

Education

2020 - Ph.D. in Mathematics, University of Pennsylvania, USA. Advisor: Robert Strain

Thesis: On The Breakdown Of Stability For The Muskat Problem And The Epitaxial Growth Equation

2013 - MSc. in Mathematics, Universidad Técnica Federico Santa María. Advisor: Eduardo Cerpa and Alberto Mercado

Thesis: Approximate Controllability of the Two Trapped Ions System

2013 - Mathematical Engineer, Universidad Técnica Federico Santa María

Publications and preprints

2026 - Cerpa E., Courdurier M., Hernández E., Medina L. E., and Paduro E. Approximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources. Discrete and Continuous Dynamical Systems, 2026, Volume 50: 69-102. https://doi.org/10.3934/dcds.2026001 . arXiv

2025 - Canelas A., Carrasco M., López J., and Paduro E. - FDIPA-SOC: A MATLAB Package for Nonlinear Second-Order Cone Programs. Comp. Appl. Math. 44, 305 (2025). https://doi.org/10.1007/s40314-025-03267-y

2025 - Courdurier M., Medina L. E., Paduro E. - Analysis of Neural Activation in Time-dependent Membrane Capacitance Models. J. Math. Biol. 90, 58 (2025), doi: 10.1007/s00285-025-02218-9 https://arxiv.org/abs/2501.17803

2024 - Cerpa E., Corrales N., Courdurier M., Medina L. E., and Paduro E. - The impact of high frequency-based stability on the onset of action potentials in neuron models. SIAM J. Appl. Math., vol. 84, no. 5, pp. 1910–1936 (2024). https://doi.org/10.1137/24M1645632 arXiv

2024 - Paduro, E. - The Second Iterate of the Muskat Equation in Supercritical Spaces. Nonlinearity. 37, 4 (2024). 10.1088/1361-6544/ad2b13 arXiv

2023 - Causade T., Paduro E., Courdurier M., Cerpa E., Grill W. M., Medina L. E. - Towards a more accurate quasi-static approximation of the electric potential for neurostimulation with kilohertz-frequency sources. J. Neural Eng. 20 066035 (2023). 10.1088/1741-2552/ad1612 BioArxiv

2023 - Cerpa E., Courdurier M., Hernández E., Medina L. E., and Paduro E. - A partially averaged system to model neuron responses to interferential current stimulation. J. Math. Biol. 86, 8 (2023). 10.1007/s00285-022-01839-8. BioArxiv

2015 - Paduro, E., Sigalotti, M. - Approximate controllability of the two trapped ions system. Quantum Inf Process 14, 2397–2418 (2015). 10.1007/s11128-015-0991-3. Arxiv

Teaching

2024/1 - Calculus III, Pontifica universidad Católica de Chile

2023/2 - Linear Algebra, Pontifica universidad Católica de Chile

2023/1 - Calculus I, Pontifica universidad Católica de Chile

2022/2 - Calculus II, Pontifica universidad Católica de Chile

2022/1 - Precalculus, Pontifica universidad Católica de Chile

2021/1 - Discrete Mathematics, Universidad Adolfo Ibañez, Chile

2018/Summer - Linear Algebra and Differential Equations, University of Pennsylvania, USA

Awards and Scholarships

2024 - ANID FONDECYT Postdoctorado 2024

2018 - Dean Scholar, University of Pennsylvania, USA

2015 - Becas Chile for PhD Students, Conicyt, Chile.

2014 - Fulbright Nomination for PhD Studies, Fulbright Foundation, Chile

2013 - Mejor Titulado de Ingeniería Matemática, Universidad Técnica Federico Santa María, Chile

2012 - National Master Scholarship, Conicyt, Chile.

2008,2011,2013 - Academic Merit Prize, Universidad Técnica Federico Santa María, Chile.

2008-2023 - Lista de Honor, Universidad Técnica Federico Santa María, Chile.

2006 - National Score in Entrance Test to Chilean Universities, Ministry of Education. Chile.

Talks

2026 - II Jornada Anual de Nuevos Edepistas, Universidad de CHile, Santiago, Chile. Slides

2025 – XCIII Encuentro anual de la Sociedad de Matemática de Chile - Analysis of Neural Activation in Time-dependent Membrane Capacitance Models. Slides

2025 – XXXVII Jornada de Matemática de la Zona Sur, Talca, Chile. Analysis of Neural Activation in Time-dependent Membrane Capacitance Models. Slides

2024 – Inverse Problems in the Physical Sciences IPPhys2024. Puerto Varas, Chile – Averaging and well-posedness in Neurostimulation. Slides

2023 - XCI Encuentro anual de la Sociedad de Matemática de Chile. Santiago, Chile – Approximation and stability results for the parabolic FitzHugh-Nagumo system with combined rapidly oscillating sources. Slides

2023 - CAGE-MAMBA seminar. Paris, France – Averaging Methods in Neurostimulation

2022 - XXX Congreso de Matemática Capricornio COMCA (online) – Ill-posedness Results for the Muskat equation

2022 - Inverse Problems: Methods, Applications & Synergies, Santiago, Chile – Interferential current stimulation for the FitzHugh-Nagumo system

2022 - Workshop in Mathematical and Computational Biology (online) – A partially averaged system to model neuron responses to interferential current stimulation. Slides

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