# Jonathan Touboul

Associate Professor of Mathematics

Degrees

École Polytechnique, Ph.D.University of Paris VI, M.S.

Expertise

Applied Mathematics, Models in Neuroscience, Dynamical Systems, Probability and Stochastic Processes.Profile

Passionate about biology and applied mathematics, my research focuses on mathematical approaches for biology, chiefly using tools from dynamical systems and stochastic theory. These two mathematical tools allow describing properties of systems evolving in time, possibly partly randomly. I have used these tools to describe the role of disorder, fluctuations and unpredictability in neural computations, with a particular interest in understanding the interplay of structure and function in the brain, from models of single cells activity up to macroscopic limits of large stochastic neuronal areas. I have also worked on the functional organization of the visual cortex in search for their organizing principles, but also on the mechanisms leading, during embryonic development, to the emergence of appropriate brain phenotypes.My approach often involves data analysis, simplified mathematical models, computer simulations and theoretical and mathematical analysis, using dynamical systems and probability. And in this program, I enthusiastically collaborate with experimentalists, mathematicians and physicists!

Courses Taught

MATH | 37a | Differential Equations |

MATH | 121a | Mathematics for Natural Sciences |

MATH | 123a | Principles of Mathematical Modeling and Applications to Biology |

MATH | 126a | Introduction to Stochastic Processes and Models |

MATH | 161a | Advanced Bifurcation Analysis in Dynamical Systems |

Scholarship

Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul and Alexandre Vidal,. "Wild oscillations in a nonlinear neuron model with resets: (Ⅰ) Bursting, spike-adding and chaos." __DCDS-B__ 22. 10 (2018): 3967-4002.

Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul and Alexandre Vidal,. "Wild oscillations in a nonlinear neuron model with resets: (Ⅱ) Mixed-mode oscillations." __DCDS-B__ 20. 10 (2018): 4003-4039.

Touboul, Jonathan and Ann Carla Staver and Simon Asher Levin. "On the complex dynamics of savanna landscapes." __Proceedings of the National Academy of Sciences USA__ N/A. N/A (2018): N/A.