PDEmas

PEOPLE

Nicolás Torres Escorza

LINES OF RESEARCH

My lines of research are Partial Differential Equations applied to population dynamics in Biology and Neuroscience, including integral-differential equations. Specifically, the dynamics of interconnected neurons and mathematical models for Alzheimer’s disease.

ARTICLES

  1. M. J. Cáceres, J. A. Cañizo, N. Torres. Comparison principles and asymptotic behavior of delayed age-structured neuron models. Preprint , 2025. Journal · arXiv
  2. N. Torres, E. Molina, L. Pujo Menjouet. An optimal control problem for anti-inflammatory treatments of Alzheimer’s disease. Prepublication Hal, 2024. Journal · arXiv
  3. M. Estavoyer, N. Torres, J. Blohm, L. Pujo Menjouet. Spatial pattern analysis of a Aβ-monomer model with inflammation processes for Alzheimer’s disease. Prepublication Hal, 2024. Journal · arXiv
  4. Torres N., Ciuperca I., Pujo Menjouet L., Matar Tine L. & Volpert V. A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease. Royal Society Open Science 11 (5), 231536, 2024. Journal · arXiv
  5. M. Sepúlveda, N. Torres, L. M. Villada. Well-posedness and numerical analysis of an elapsed time model with strongly coupled neural networks. arXiv preprint arXiv:2310.02068, 2023. Journal · arXiv
  6. Torres N., Perthame B. & Salort, D. A multiple time renewal equation for neural assemblies with elapsed time model. Nonlinearity 35(10):5051–5075, 2022. Journal · arXiv
  7. N. Torres. Asymptotic behavior of solutions of the elapsed time model for neural assemblies. Sorbonne Université, 2021. Journal · arXiv
  8. Torres, N., Cáceres, M. J., Perthame, B., Salort, D. An elapsed time model for strongly coupled inhibitory and excitatory neural networks. Physica D: Nonlinear Phenomena: 132977, 2021. Journal · arXiv
  9. Torres N., & Salort D. Dynamics of Neural Networks with Elapsed Time Model and Learning Processes. Acta Applicandae Mathematicae, 1-35, 2020. Journal · arXiv
  10. Cantrell R. S., Cosner, C. Martínez S. & Torres N. On a competitive system with ideal free dispersal. Journal of Differential Equations 265(8), 3464-3493, 2018. Journal · arXiv

PARTICIPATION IN CONFERENCES

These are the most recent conferences i have participated in during the last 10 years:

  1. Topics on Neuroscience, Collective Migration and Parameter Estimation. University of Oxford, United Kingdom, 2023.
  2. Seminar CAPDE. University of Chile – CMM, 2016, 2018, 2020 and 2022.
  3. Mathematical modeling and statistical analysis in neuroscience. IHP, France, 2022.
  4. Young Researchers Workshop on Probability and PDEs. University of Granada – IMAG, Spain, 2022.
  5. Escuela de investigación en teoría cinética. CIRM, France, 2022.
  6. Conference SMAI 2021. France, 2021.
  7. VI Southern-Summer School on Mathematical Biology. UNESP, Brazil, 2017.