Speakers
Description
Mean-field limits of neural assemblies lead to nonlinear partial differential equations (PDEs) that have attracted considerable interest in recent years; see, for instance, the recent survey \cite{CR2025}. This interest stems from the fact that these equations raise several highly challenging mathematical questions within an unconventional formal framework, including the existence and uniqueness of solutions, finite-time blow-up, periodic solutions, and, more generally, long-time behavior and pattern formation. Beyond these theoretical issues, this important subject is also motivated by the investigation of qualitative properties of neural systems, including the emergence of rhythmic activity and synchronization, as well as by comparisons with experimental observations.
Four outstanding speakers have agreed to present their recent results: P. Roux (Lyon) \cite{IRSS2022}, D. Salort (Paris) \cite{PRS2025}, S. Solem (Oslo) \cite{CHS2022}, Z. Zhou (Westlake) \cite{DouZhou2025}. They have contributed recently with several original contributions covering a wide range of subjects in the field of PDEs for neuroscience.
Bibliography
@article{PRS2025,
author = {Perthame, Beno{\^{\i}}t and Rieutord, Cl{\'e}ment and Salort, Delphine},
title = {Strongly nonlinear age-structured equation, time-elapsed model and large delays},
fjournal = {Journal of Mathematical Biology},
journal = {J. Math. Biol.},
issn = {0303-6812},
volume = {91},
number = {5},
pages = {29},
note = {Id/No 65},
year = {2025},
language = {English},
doi = {10.1007/s00285-025-02294-x},
keywords = {35B10,35B40,35Q49,92D25},
zbMATH = {8113917}
}
@article{CHS2022,
author = {Carrillo, Jos{\'e} A. and Holden, Helge and Solem, Susanne},
title = {Noise-driven bifurcations in a neural field system modelling networks of grid cells},
fjournal = {Journal of Mathematical Biology},
journal = {J. Math. Biol.},
issn = {0303-6812},
volume = {85},
number = {4},
pages = {30},
note = {Id/No 42},
year = {2022},
language = {English},
doi = {10.1007/s00285-022-01811-6},
keywords = {92B20,35Q92,35B32},
zbMATH = {7600566},
Zbl = {1500.92004}
}
@article{DouZhou2025,
author = {Dou, Xu'an and Zhou, Zhennan},
title = {Dilating blow-up time: a generalized solution of the {NNLIF} neuron model and its global well-posedness},
fjournal = {Communications in Mathematical Sciences},
journal = {Commun. Math. Sci.},
issn = {1539-6746},
volume = {23},
number = {4},
pages = {1081--1138},
year = {2025},
language = {English},
doi = {10.4310/CMS.250412104353},
keywords = {35Q84,35A09,35B44,35D99,35Q92,92B20},
zbMATH = {8050032},
Zbl = {1564.35264}
}
@article{CR2025,
author = {Carrillo, Jos{\'e} A. and Roux, Pierre},
title = {Nonlinear partial differential equations in neuroscience: from modeling to mathematical theory},
fjournal = {M(^3)AS. Mathematical Models \& Methods in Applied Sciences},
journal = {Math. Models Methods Appl. Sci.},
issn = {0218-2025},
volume = {35},
number = {2},
pages = {403--584},
year = {2025},
language = {English},
doi = {10.1142/S0218202525400044},
keywords = {35-02,92-02,35Q49,35Q84,35B40,65C30},
zbMATH = {8023785},
Zbl = {1562.35002}
}
@article {IRSS2022,
AUTHOR = {Ikeda, Kota and Roux, Pierre and Salort, Delphine and Smets,
Didier},
TITLE = {Theoretical study of the emergence of periodic solutions for
the inhibitory {NNLIF} neuron model with synaptic delay},
JOURNAL = {Math. Neurosci. Appl.},
FJOURNAL = {Mathematical Neuroscience and Applications},
VOLUME = {2},
YEAR = {2022},
PAGES = {Art. No. 4, 37},
MRCLASS = {92B20 (35B10 35K20 92B25)},
MRNUMBER = {4665143},
MRREVIEWER = {Shangjiang Guo},
}
