Esteban Paduro


Since 2021 postdoc at Pontifica Universidad Católica  de Chile

Funded by ANID FONDECYT postdoctoral.

email: esteban.paduro (at) gmail

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 Tecnica Federico Santa Maria. 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

2024 - (preprint) Canelas A., Carrasco M., López J. and Paduro E. - FDIPA-SOC: A MATLAB Package for Nonlinear Second-Order Cone Programs. 

2024 - (Accepted) 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 Journal on Applied Mathematics.  arXiv

2023 - (Preprint) 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. 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.